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by Huong Ha; James S. Welsh; Cristian R. Rojas; Bo Wahlberg
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In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound for the traditional SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.09351
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For a multinormal distribution with a $p$-dimensional mean vector ${\mbtheta}$ and an arbitrary unknown dispersion matrix ${\mbSigma}$, Rao ([9], [10]) proposed two tests for the problem of testing $ H_{0}:{\mbtheta}_{1} = {\bf 0}, {\mbtheta}_{2} = {\bf 0}, {\mbSigma}~ \hbox{unspecified},~\hbox{versus}~H_{1}:{\mbtheta}_{1} \ne {\bf 0}, {\mbtheta}_{2} ={\bf 0}, {\mbSigma}~\hbox{unspecified}$, where ${\mbtheta}^{'}=({\mbtheta}^{'}_{1},{\mbtheta}^{'}_{2})$. These tests are referred to as Rao's...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.00530
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In this article, weak convergence of the general non-Markov state transition probability estimator by Titman (2015) is established which, up to now, has not been verified for any other general such non-Markov estimator currently in the literature. A similar theorem is shown for the bootstrap, yielding resampling-based inference methods for statistical functionals. Formulas of the involved covariance functions are presented in detail. As a particular application, the conditional expected length...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.03304
Arxiv.org
by Angelo Mele; Lingjiong Zhu
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We study an equilibrium model of sequential network formation with heterogeneous players. The payoffs depend on the number and composition of direct connections, but also the number of indirect links. We show that the network formation process is a potential game and in the long run the model converges to an exponential random graph (ERGM). Since standard simulation-based inference methods for ERGMs could have exponentially slow convergence, we propose an alternative deterministic method, based...
Topics: Other Statistics, Statistics, Methodology
Source: http://arxiv.org/abs/1702.00308
Arxiv.org
by Adityanand Guntuboyina; Donovan Lieu; Sabyasachi Chatterjee; Bodhisattva Sen
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We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer $r \geq 1$, the trend filtering estimator of order $r$ is defined as the minimizer of the sum of squared errors when we constrain (or penalize) the sum of the absolute discrete derivatives of order $r$ over the input points. For $r = 1$, the estimator reduces to total variation regularization which has received much attention in the statistics and image processing literature. In...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.05113
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by John Urschel; Victor-Emmanuel Brunel; Ankur Moitra; Philippe Rigollet
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Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are fast algorithms for sampling, marginalization and conditioning, much less is known about learning the parameters of a DPP. Our contribution is twofold: (i) we establish the optimal sample complexity achievable in this problem and show that it is governed by...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.00539
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by Alexandre Belloni; Victor Chernozhukov; Abhishek Kaul
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We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to avoid non-vanishing biases in addition to handle the high dimensionality of the parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. Our main contribution complements this literature with the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.00469
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by Ester Mariucci; Kolyan Ray; Botond Szabo
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The estimation of a log-concave density on $\mathbb{R}$ is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.09531
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by Esmaeil Bashkar; Hamzeh Torabi; Majid Asadi
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In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the likelihood ratio order. In the presence of the Archimedean copula, we study stochastic comparison of series dependent systems in terms of the usual stochastic order.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06329
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by R. Arnold; P. E. Jupp; H. Schaeben
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The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.01579
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by Xi Chen; Weidong Liu
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Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate the problem of testing independence among columns under the matrix-variate normal modeling of data. We propose a computationally simple and tuning-free test statistic, characterize its limiting null distribution, analyze the statistical power and prove its...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.08843
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When considering two or more time series of functions or curves, for instance those derived from densely observed intraday stock price data of several companies, the empirical cross-covariance operator is of fundamental importance due to its role in functional lagged regression and exploratory data analysis. Despite its relevance, statistical procedures for measuring the significance of such estimators are undeveloped. We present methodology based on a functional central limit theorem for...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.00315
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This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate under various metrics, density derivative estimation, and bandwidth selection. Then, we introduce common approaches to the construction of confidence intervals/bands, and we discuss how to handle bias. Next, we talk about recent advances in the inference of...
Topics: Other Statistics, Statistics, Methodology
Source: http://arxiv.org/abs/1704.03924
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by Holger Dette; Josua Gösmann
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This paper investigates the problem of detecting relevant change points in the mean vector, say $\mu_t =(\mu_{1,t},\ldots ,\mu_{d,t})^T$ of a high dimensional time series $(Z_t)_{t\in \Z}$. While the recent literature on testing for change points in this context considers hypotheses for the equality of the means $\mu_h^{(1)}$ and $\mu_h^{(2)}$ before and after the change points in the different components, we are interested in a null hypothesis of the form $$ H_0: |\mu^{(1)}_{h} - \mu^{(2)}_{h}...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.04614
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In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other observables. This method sums over different model parameter combinations but does not require the need for making assumptions on priors or underlying probability functions. Moreover, by construction the results are invariant under reparametrization of the model...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.07195
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Although there is no shortage of clustering algorithms proposed in the literature, the question of the most relevant strategy for clustering compositional data (i.e., data made up of profiles, whose rows belong to the simplex) remains largely unexplored in cases where the observed value of an observation is equal or close to zero for one or more samples. This work is motivated by the analysis of two sets of compositional data, both focused on the categorization of profiles but arising from...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06150
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by Igor Vladimirovich Rodionov
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The goodness-of-fit test for discrimination of two tail distribution using higher order statistics is proposed. The consistency of proposed test is proved for two different alternatives. We do not assume belonging the corresponding distribution function to a maximum domain of attraction.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.05641
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by Pierre Del Moral; Adrian N. Bishop
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Let ${\cal X }=XX^{\prime}$ be a random matrix associated with a centered $r$-column centered Gaussian vector $X$ with a covariance matrix $P$. In this article we compute expectations of matrix-products of the form $\prod_{1\leq i\leq n}({\cal X } P^{v_i})$ for any $n\geq 1$ and any multi-index parameters $v_i\in\mathbb{N}$. We derive closed form formulae and a simple sequential algorithm to compute these matrices w.r.t. the parameter $n$. The second part of the article is dedicated to a non...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.00353
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by Ignacio Cascos; Ilya Molchanov
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Bands of vector-valued functions $f:T\mapsto\mathbb{R}^d$ are defined by considering convex hulls generated by their values concatenated at $m$ different values of the argument. The obtained $m$-bands are families of functions, ranging from the conventional band in case the time points are individually considered (for $m=1$) to the convex hull in the functional space if the number $m$ of simultaneously considered time points becomes large enough to fill the whole time domain. These bands give...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.09269
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Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a pre-asymptotic version for such observation schemes. For max-stable processes with Fr{\'e}chet margins we...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.05656
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In this paper, we focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type $(a,b,0)$ class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show abundant distributional properties such as overdispersion and underdispersion, log-concavity, log-convexity (infinite divisibility), pseudo compound Poisson, stochastic ordering and asymptotic approximation. Some characterizations including sum of...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.05050
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This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown, but assume that there is an independent sample from the measurement error distribution. The sample from the measurement error distribution need not be independent from the sample on response and predictor variables. The availability of a sample from the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.03377
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by Catherine Aaron; Alejandro Cholaquidis; Antonio Cuevas
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This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set $S \subset {\mathbb R}^d$. The general aim is to identify (via stochastic procedures) some qualitative or quantitative features of $S$, of geometric or topological character. The available information is just a random sample of points drawn on $S$. The term "to identify" means here to achieve a correct answer almost surely (a.s.)...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.05193
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by Cornelia Wichelhaus; Moritz von Rohrscheidt
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In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other characteristics of the system, particular interest is in the waiting time distribution which is not accessible in closed form. Thus, we use an indirect statistical approach by exploiting the Pollaczek-Khinchine transform formula for the Laplace transform of the waiting...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.07072
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This paper studies the minimum distance estimation problem for panel data model. We propose the minimum distance estimators of regression parameters of the panel data model and investigate their asymptotic distributions. This paper contains two main contributions. First, the domain of application of the minimum distance estimation method is extended to the panel data model. Second, the proposed estimators are more efficient than other existing ones. Simulation studies compare performance of the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.07044
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We propose an objective prior distribution on correlation kernel parameters for Simple Kriging models in the spirit of reference priors. Because it is proper and defined through its conditional densities, it and its associated posterior distribution lend themselves well to Gibbs sampling, thus making the full-Bayesian procedure tractable. Numerical examples show it has near-optimal frequentist performance in terms of prediction interval coverage
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.07233
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We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In the above circumstance, narrow convergence with respect to uniform convergence fails to hold, because of the strength of it's topology. A new approach we propose to the lack-of-uniform-convergence is based on Mosco-convergence that is weaker topology than...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.02840
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by Alexander Luedtke; Antoine Chambaz
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This article improves the existing proven rates of regret decay in optimal policy estimation. We give a margin-free result showing that the regret decay for estimating a within-class optimal policy is second-order for empirical risk minimizers over Donsker classes, with regret decaying at a faster rate than the standard error of an efficient estimator of the value of an optimal policy. We also give a result from the classification literature that shows that faster regret decay is possible via...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06431
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The models considered in this paper are a special subclass of Relational models which may be appropriate when a collection of independence statements must hold even after probabilities are re-scaled to sum to 1. After reviewing the basic properties of these models and deriving some new ones, two algorithms for computing maximum likelihood estimates are presented. Some new light is also thrown on the underlying geometry.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06762
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This paper studies some robust regression problems associated with the $q$-norm loss ($q\ge1$) and the $\epsilon$-insensitive $q$-norm loss in the reproducing kernel Hilbert space. We establish a variance-expectation bound under a priori noise condition on the conditional distribution, which is the key technique to measure the error bound. Explicit learning rates will be given under the approximation ability assumptions on the reproducing kernel Hilbert space.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.01956
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by Johannes T. N. Krebs
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In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in highly-connected networks. It can be useful to obtain consistency properties for nonparametric estimators of conditional expectation functions which are derived from such networks.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04188
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by Mehmet Caner
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We provide a new version of delta theorem, that takes into account of high dimensional parameter estimation. We show that depending on the structure of the function, the limits of functions of estimators have faster or slower rate of convergence than the limits of estimators. We illustrate this via two examples. First, we use it for testing in high dimensions, and second in estimating large portfolio risk. Our theorem works in the case of larger number of parameters, $p$, than the sample size,...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.05911
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by Michael Falk; Florian Wisheckel
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It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases. We extend this result to bivariate random variables, where the os are taken componentwise. An explicit representation of the conditional distribution of bivariate os turns out to be a powerful tool.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.09108
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This paper provides conditions under which a non-stationary copula-based Markov process is $\beta$-mixing. We introduce, as a particular case, a convolution-based gaussian Markov process which generalizes the standard random walk allowing the increments to be dependent.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01458
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Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be restricted in that the similar density contours ought to be elliptical. Kamiya, Takemura and Kuriki [Star-shaped distributions and their generalizations, Journal of Statistical Planning and Inference 138 (2008), 3429--3447] proposed star-shaped distributions, for...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.05994
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target intensity through contamination with additive error. Under the assumption that the error distribution is unknown and only available by means of an additional sample $Y_1,\ldots,Y_m$ we derive minimax rates of convergence with respect to the sample sizes $n$...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.05619
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by Alexander V. Kolnogorov
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We consider the two-armed bandit problem as applied to data processing if there are two alternative processing methods available with different a priori unknown efficiencies. One should determine the most effective method and provide its predominant application. Gaussian two-armed bandit describes the batch, and possibly parallel, processing when the same methods are applied to sufficiently large packets of data and accumulated incomes are used for the control. If the number of packets is large...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.03631
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by Ulrich Faigle; Gerhard Gierz
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A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes between the deterministic evolution of a system and the stochastic nature of observations on the evolving system. General Markov chains are defined in this context and it is shown how typical traditional models of classical or quantum random walks and Markov...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.06140
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by Dennis Leung; Qi-Man Shao
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Let ${\bf R}$ be the Pearson correlation matrix of $m$ normal random variables. The Rao's score test for the independence hypothesis $H_0 : {\bf R} = {\bf I}_m$, where ${\bf I}_m$ is the identity matrix of dimension $m$, was first considered by Schott (2005) in the high dimensional setting. In this paper, we study the asymptotic minimax power function of this test, under an asymptotic regime in which both $m$ and the sample size $n$ tend to infinity with the ratio $m/n$ upper bounded by a...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.07249
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by Abdollah Jalilian; Yongtao Guan; Rasmus Waagepetersen
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The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimators are popular but especially for clustered point patterns suffer from bias for small spatial lags. In this paper we introduce a new orthogonal series estimator. The new...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.01736
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by Luca Weihs; Bill Robinson; Emilie Dufresne; Jennifer Kenkel; Kaie Kubjas; Reginald L. McGee; Nhan Nguyen; Elina Robeva; Mathias Drton
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Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.03884
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by Peng Ding; Xinran Li; Luke W. Miratrix
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There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite populations, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the physical randomization of the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.08615
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by Xi Chen; Adityanand Guntuboyina; Yuchen Zhang
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We study the problem of estimating an unknown vector $\theta$ from an observation $X$ drawn according to the normal distribution with mean $\theta$ and identity covariance matrix under the knowledge that $\theta$ belongs to a known closed convex set $\Theta$. In this general setting, Chatterjee (2014) proved that the natural constrained least squares estimator is "approximately admissible" for every $\Theta$. We extend this result by proving that the same property holds for all convex...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.00542
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This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a class is assumed to be intersection stable. No further hypotheses on the boundary of the set are imposed; in particular, the convex sets and the so-called weakly-convex sets are covered by the framework. The approach rests upon a homogeneous Poisson point...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.01658
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by Ismaël Castillo; Peter Orbanz
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We consider estimation of certain functionals of random graphs. The random graph is generated by a stochastic block model (SBM). The number of classes is fixed or grows with the number of vertices. Minimax lower and upper bounds of estimation along specific submodels are derived. The results are nonasymptotic and imply that uniform estimation of a single connectivity parameter is much slower than the expected asymptotic pointwise rate. Specifically, the uniform quadratic rate does not scale as...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.03412
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by Jinzhu Jia; Fang Xie; Lihu Xu
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We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We show that under mild conditions, our estimator is $\ell_1$ consistent and the tuning parameter can be pre-specified, which shares the same good property of the square-root Lasso.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.03965
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by Guangyu Zhu; Jiahua Chen
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Multi-parameter one-sided hypothesis test problems arise naturally in many applications. We are particularly interested in effective tests for monitoring multiple quality indices in forestry products. Our search reveals that there are many effective statistical methods in the literature for normal data, and that they can easily be adapted for non-normal data. We find that the beautiful likelihood ratio test is unsatisfactory, because in order to control the size, it must cope with the least...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.04799
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by Sunanda Bagchi
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In Bagchi (2010) main effect plans "orthogonal through the block factor" (POTB) have been constructed. The main advantages of a POTB are that (a) it may exist in a set up where an "usual" orthogonal main effect plan (OMEP) cannot exist and (b) the data analysis is nearly as simple as an OMEP. In the present paper we extend this idea and define the concept of orthogonality between a pair of factorial effects ( main effects or interactions) "through the block factor"...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.03212
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by Michael Hoffmann; Mathias Vetter; Holger Dette
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In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localisation of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analyzed...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.04040
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by Dimbihery Rabenoro
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We present a functional form of the Erd\"os-Renyi law of large numbers for Levy processes.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06521
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by Elizabeth Gross; Sonja Petrović; Donald Richards; Despina Stasi
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Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum likelihood estimators using hill-climbing algorithms, and consequent difficulties in the resulting statistical inference. In this paper, we study the multiple roots phenomenon in maximum likelihood estimation for factor analysis. We prove that the corresponding...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.04477
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A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution is near to familiar distributions like the gamma and log-normal distributions, but this new one shows own elements and thus does not generalize neither of these distributions. Hence, the new distribution constitutes a new alternative to fit values showing...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04880
Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for their averaged version in general Hilbert spaces. Moreover, since having the asymptotic normality of estimates is often unusable without an estimation of the asymptotic variance, we introduce a recursive algorithm of the asymptotic variance of the averaged...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00931
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A wide variety of phenomena of engineering and scientific interest are of a continuous-time nature and can be modeled by stochastic differential equations (SDEs), which represent the evolution of the uncertainty in the states of a system. For systems of this class, some parameters of the SDE might be unknown and the measured data often includes noise, so state and parameter estimators are needed to perform inference and further analysis using the system state path. The distributions of SDEs...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01847
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by Natalia Markovich
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Regarding the analysis of Web communication, social and complex networks the fast finding of most influential nodes in a network graph constitutes an important research problem. We use two indices of the influence of those nodes, namely, PageRank and a Max-linear model. We consider the PageRank %both as %Galton-Watson branching process and as an autoregressive process with a random number of random coefficients that depend on ranks of incoming nodes and their out-degrees and assume that the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01302
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by Markus Bibinger; Christopher Neely; Lars Winkelmann
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An extensive empirical literature documents a generally negative correlation, named the "leverage effect" between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect --- that is, a relation between contemporaneous jumps in prices and volatility --- in high-frequency data with market microstructure...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06537
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by Valentin Patilea; Ingrid Van Keilegom
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In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be `cured'. The population is thus a mixture of two subpopulations: the one of cured subjects, and the one of `susceptible' subjects. When covariates are present, a so-called mixture cure model can be used to model the conditional survival function of the population. It depends on two components: the probability of being cured and the conditional survival function...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.03769
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We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. In Part I the original pointwise selection rule from a family of "kernel-type" estimators is proposed. For the selected estimator, we prove an $\bL_p$-norm oracle inequality and...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.04418
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This paper deals with asymptotics for multiple-set linear canonical analysis (MSLCA). A definition of this analysis, that adapts the classical one to the context of Euclidean random variables, is given and properties of the related canonical coefficients are derived. Then, estimators of the MSLCA's elements, based on empirical covariance operators, are proposed and asymptotics for these estimators are obtained. More precisely, we prove their consistency and we obtain asymptotic normality for...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06428
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by Taku Moriyama; Yoshihiko Maesono
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We propose new smoothed median and the Wilcoxon's rank sum test. As is pointed out by Maesono et al.(2016), some nonparametric discrete tests have a problem with their significance probability. Because of this problem, the selection of the median and the Wilcoxon's test can be biased too, however, we show new smoothed tests are free from the problem. Significance probabilities and local asymptotic powers of the new tests are studied, and we show that they inherit good properties of the discrete...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.07977
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by Alfredo Alegría; Emilio Porcu; Reinhard Furrer; Jorge Mateu
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The construction of valid and flexible cross-covariance functions is a fundamental task for modelling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance structure allows to capture both the space-time dependencies between the observations and the development of accurate predictions. For data observed over large portions of planet Earth it is necessary to take into account the curvature of the planet. Hence...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.06010
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In this paper we show that the negative sample distance covariance function is a quasi-concave set function of samples of random variables that are not statistically independent. We use these properties to propose greedy algorithms to combinatorially optimize some diversity (low statistical dependence) promoting functions of distance covariance. Our greedy algorithm obtains all the inclusion-minimal maximizers of this diversity promoting objective. Inclusion-minimal maximizers are multiple...
Topics: Other Statistics, Statistics, Methodology
Source: http://arxiv.org/abs/1702.05340
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by H. N. Nagaraja; Karthik Bharath; Fangyuan Zhang
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We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of $X_{k:n}$. For an extreme $X_{k:n}$, the asymptotic independence property...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.05910
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by Alexandra Carpentier; Nicolas Verzelen
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Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of |{\theta}|_0 as a multiple testing problem of all hypotheses {|{\theta}|_0
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.00167
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by Helena Ferreira; Marta Ferreira
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A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the extremal index appears as a key parameter to capture the effect of temporal dependence on the limiting distribution of the maxima. The multivariate extremal index corresponds to a generalization of this concept to a multivariate context and affects the tail...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.01696
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by Markus Reiss; Johannes Schmidt-Hieber
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Given a sample of a Poisson point process with intensity $\lambda_f(x,y) = n \mathbf{1}(f(x) \leq y),$ we study recovery of the boundary function $f$ from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We derive contraction rates with respect to the $L^1$-norm for several classes of priors, including Gaussian priors, priors based on (truncated) random series, compound Poisson processes, and subordinators. We also investigate the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.08358
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by Herwig Wendt; Gustavo Didier; Sébastien Combrexelle; Patrice Abry
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While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not determined by that of the individual components. To model this situation in a versatile manner, we introduce a class of multivariate Gaussian stochastic processes called Hadamard fractional Brownian motion (HfBm). Its theoretical study sheds light on the issues...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04366
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We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart, [Statist. Probab. Lett., 80 (2010), 1030-1038] to a special 2-dimensions. The strategy is to exploit the Garsia-Rodemich-Rumsey inequality and complex fourth moment theorems. The main ingredients of this paper are the sample path regularity of a multiple Wiener-Ito...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.07568
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Data with hierarchical structure arise in many fields. Estimating global effect sizes from nested data, and testing effects against global null hypotheses, is, however, more challenging than in the traditional setting of independent and identically distributed data. In this paper, we review statistical approaches to deal with nested data following either a fixed-effect or a random-effects model. We focus on methods that are easy to implement, such as group-level t-tests and Stouffer's method....
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.03476
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by Debraj Das; Karl Gregory; S. N. Lahiri
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The Adaptive LASSO (ALASSO) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] as a modification of the LASSO for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou (2006) established that the ALASSO estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain fixed-dimensional settings. In an influential paper, Minnier,...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1703.03165
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by Huiming Zhang; Bo Li; G. Jay Kerns
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In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller's characterization of discrete infinitely divisible distributions to signed discrete infinitely divisible distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the L\'evy-Wiener theorem. This is a special case of an open problem which is proposed by Sato(2014), Chaumont and Yor(2012). An analogous result...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.03892
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by Peng Ding; Tyler VanderWeele; James Robins
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Drawing causal inference with observational studies is the central pillar of many disciplines. One sufficient condition for identifying the causal effect is that the treatment-outcome relationship is unconfounded conditional on the observed covariates. It is often believed that the more covariates we condition on, the more plausible this unconfoundedness assumption is. This belief has had a huge impact on practical causal inference, suggesting that we should adjust for all pretreatment...
Topics: Statistics Theory, Statistics, Applications, Mathematics
Source: http://arxiv.org/abs/1701.04177
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by Véronique Maume-Deschamps; Ibrahima Niang
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The paper concerns quantile oriented sensitivity analysis. We rewrite the corresponding indices using the Conditional Tail Expectation risk measure. Then, we use this new expression to built estimators.
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00925
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by Piotr Graczyk; Hideyuki Ishi; Salha Mamane
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Let G = An be the graph corresponding to the graphical model of nearest neighbour interaction in a Gaussian character. We study Natural Exponential Families( NEF) ofWishart distributions on convex cones QG and PG, where PG is the cone of positive definite real symmetric matrices with obligatory zeros prescribed by G, and QG is the dual cone of PG. The Wishart NEF that we construct include Wishart distributions considered earlier by Lauritzen (1996) and Letac and Massam (2007) for models based...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.04065
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by Katharina Strohriegl
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An important property of statistical estimators is qualitative robustness, that is small changes in the distribution of the data only result in small chances of the distribution of the estimator. Moreover, in practice, the distribution of the data is commonly unknown, therefore bootstrap approximations can be used to approximate the distribution of the estimator. Hence qualitative robustness of the statistical estimator under the bootstrap approximation is a desirable property. Currently most...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.05933
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The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient matrix. We propose multivariate bootstrap techniques as a means for making inferences about the unknown regression coefficient matrix. These bootstrapping techniques are extensions of those developed in Freedman (1981), which are only appropriate for...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1704.07040
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It has been shown that the nonreversible overdamped Langevin dynamics enjoy better convergence properties in terms of spectral gap and asymptotic variance than the reversible one. In this article we propose a variance reduction method for the Metropolis-Hastings Adjusted Langevin Algorithm (MALA) that makes use of the good behaviour of the these nonreversible dynamics. It consists in constructing a nonreversible Markov chain (with respect to the target invariant measure) by using a Generalized...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.05833
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by Yoav Zemel; Victor M. Panaretos
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We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and point processes. We elucidate how the two problems are linked, each being in a sense dual to the other. We first study the finite sample version of the problem in the continuum. Exploiting the tangent bundle structure of Wasserstein space,...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.06876
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by Mareile Große Ruse; Adeline Samson; Susanne Ditlevsen
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Modeling of longitudinal data often requires diffusion models that incorporate overall time-dependent, nonlinear dynamics of multiple components and provide sufficient flexibility for subject-specific modeling. This complexity challenges parameter inference and approximations are inevitable. We propose a method for approximate maximum-likelihood parameter estimation in multivariate time-inhomogeneous diffusions, where subject-specific flexibility is accounted for by incorporation of...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.08284
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by Richard A. Lockhart; Richard J. Samworth
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We provide some comments on the article `High-dimensional simultaneous inference with the bootstrap' by Ruben Dezeure, Peter Buhlmann and Cun-Hui Zhang.
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1703.10143
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by Stanislav Volgushev; Shih-Kang Chao; Guang Cheng
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The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated quantile curves. Our...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.06088
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by Mauricio Sadinle; Jerome P. Reiter
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With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the analyst to impose restrictions that make the models uniquely obtainable from the distribution of the observed data. We present an approach for constructing classes of identifiable nonignorable missing data models. The main idea is to use a sequence of carefully...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.01395
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by Yong Zhang; Xiaodi Qian; Hong Qin; Ting Yan
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Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this paper, we study an affiliation model with the degree sequence as the exclusively...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.01906
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We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.07281
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by Binhuan Wang; Yixin Fang; Heng Lian; Hua Liang
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We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each sub-population. This work generalizes the partially linear framework proposed in Zhao et al. (2016), which considers only one common feature. Motivated by Zhao et al. (2016), we propose an aggregation type of estimators for the commonality parameters that possess the...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.03772
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by Jianqing Fan; Dong Wang; Kaizheng Wang; Ziwei Zhu
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Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distributed algorithms for PCA are thus needed. This paper proposes and studies a distributed PCA algorithm: each node machine computes the top $K$ eigenvectors and transmits them to the...
Topics: Computation, Statistics, Statistics Theory, Mathematics
Source: http://arxiv.org/abs/1702.06488
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by Achmad Choiruddin; Jean-François Coeurjolly; Frédérique Letué
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This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood and logistic regression likelihood. We provide general conditions on the spatial point processes and on penalty functions which ensure consistency, sparsity and asymptotic normality. We discuss the numerical implementation and assess finite sample properties...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1703.02462
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This paper shows that the Conditional Quantile Treatment Effect on the Treated can be identified using a combination of (i) a conditional Distributional Difference in Differences assumption and (ii) an assumption on the conditional dependence between the change in untreated potential outcomes and the initial level of untreated potential outcomes for the treated group. The second assumption recovers the unknown dependence from the observed dependence for the untreated group. We also consider...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.03618
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We consider the first exit time of a Shiryaev-Roberts diffusion with constant positive drift from the interval $[0,A]$ where $A>0$. We show that the moment generating function (Laplace transform) of a suitably standardized version of the first exit time converges to that of the unit-mean exponential distribution as $A\to+\infty$. The proof is explicit in that the moment generating function of the first exit time is first expressed analytically and in a closed form, and then the desired limit...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.08900
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by Robert J. Adler; Sarit Agami; Pratyush Pranav
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Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this challenge is `TDA', or `Topological Data Analysis', one of the primary aims of which is providing non-metric, but topologically informative, pre-analyses of data sets which make later, more quantitative analyses feasible. While TDA rests on strong mathematical...
Topics: Other Statistics, Statistics, Applications, Methodology
Source: http://arxiv.org/abs/1704.08248
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by Lev B. Klebanov; Jaromir Antoch; Andrea Karlova; Ashot V. Kakosyan
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We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order to avoid the occurance of the outliers. We observe that some variants of the outliers lead to classical results in probability, such as the law of large numbers and the concept of heavy tailed distributions. Key words: outlier; the law of large numbers; heavy...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.06642
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by Javier Hidalgo; Jungyoon Lee; Myung Hwan Seo
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This paper is concerned with inference in regression models with either a kink or a jump at an unknown threshold, particularly when we do not know whether the kink or jump is the true specification. One of our main results shows that the statistical properties of the estimator of the threshold parameter are substantially different under the two settings, with a slower rate of convergence under the kink design, and more surprisingly slower than if the correct kink specification were employed in...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.00836
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The two-level normal hierarchical model (NHM) has played a critical role in the theory of small area estimation (SAE), one of the growing areas in statistics with numerous applications in different disciplines. In this paper, we address major well-known shortcomings associated with the empirical best linear unbiased prediction (EBLUP) of a small area mean and its mean squared error (MSE) estimation by considering an appropriate model variance estimator that satisfies multiple properties. The...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1701.04176
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When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by some selection (screening or filtering) process, and then to simultaneously test the selected hypotheses. The main advantage of this strategy is to greatly reduce the severe effect of high dimensions. However, the first screening or selection stage must be properly accounted for in order to maintain some type of error...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1703.06336
We prove an exponential deviation inequality for the convex hull of a finite sample of i.i.d. random points with a density supported on an arbitrary convex body in $\R^d$, $d\geq 2$. When the density is uniform, our result yields rate optimal upper bounds for all the moments of the missing volume of the convex hull, uniformly over all convex bodies of $\R^d$: We make no restrictions on their volume, location in the space or smoothness of their boundary. After extending an identity due to Efron,...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01620
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by Matias D. Cattaneo; Michael Jansson; Kenichi Nagasawa
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This note proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975) and the isotonic density estimator of Grenander (1956). In both cases, the standard nonparametric bootstrap is known to be inconsistent. Our method restores consistency of the nonparametric bootstrap by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1704.08066
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by Qingguo Tang; Linglong Kong; David Ruppert; Rohana J. Karunamuni
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This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is suitable for more complicated data structures. However, its estimation inherits the difficulties and complexities from both components and makes it a challenging problem, which calls for new methodology. We propose a novel profile B-spline method to estimate...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1703.02736
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This paper considers the problem of inliers and empty cells and the resulting issue of relative inefficiency in estimation under pure samples from a discrete population when the sample size is small. Many minimum divergence estimators in the $S$-divergence family, although possessing very strong outlier stability properties, often have very poor small sample efficiency in the presence of inliers and some are not even defined in the presence of a single empty cell; this limits the practical...
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1702.03557
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We propose an optimal experimental design for a curvilinear regression model that minimizes the band-width of simultaneous confidence bands. Simultaneous confidence bands for nonlinear regression are constructed by evaluating the volume of a tube about a curve that is defined as a trajectory of a regression basis vector (Naiman, 1986). The proposed criterion is constructed based on the volume of a tube, and the corresponding optimal design is referred to as the minimum-volume optimal design....
Topics: Statistics Theory, Statistics, Methodology, Mathematics
Source: http://arxiv.org/abs/1704.03995
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by Pradip Kundu; Asok K. Nanda
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The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as Marshall-Olkin family of distributions or Marshall-Olkin extended distributions. In this paper, we consider Marshall-Olkin family of distributions in discrete case with fixed tilt parameter. We study different ageing properties, as well as different stochastic...
Topics: Probability, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00141