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Arxiv.org
by Azka Javaid; Xiaofei Wang; Nicholas J Horton
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One learning goal of the introductory statistics course is to develop the ability to make sense of research findings in published papers. The Atlantic magazine regularly publishes a feature called "Study of Studies" that summarizes multiple articles published in a particular domain. We describe a classroom activity to develop this capacity using the "Study of Studies." In this activity, students read capsule summaries of twelve research papers related to restaurants and...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1701.08438
Arxiv.org
by Nanjing Jian; Shane G. Henderson
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Consider a real-valued function that can only be observed with stochastic simulation noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function values at the design points. We develop an asymptotically consistent Bayesian sequential sampling procedure that estimates the posterior probability of this being true. In each iteration, the posterior probability is estimated using Monte Carlo...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1703.04185
Arxiv.org
by Kayvan Sadeghi
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A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special case. We exploit a generalization of ordering, called preordering, of the nodes of (mixed) graphs....
Topics: Other Statistics, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.08366
Arxiv.org
by R. Sharma
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It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1704.06292
Arxiv.org
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Malaysian Airlines flight MH370 veered off course unexpectedly during a scheduled trip from Kuala Lumpur to Beijing on the 7th of March 2014. MH370 was tracked via military radar into the Malacca Straits and after disappearing from radar was believed to have turned south towards the southern Indian Ocean before crashing approximately six hours later. This article presents details of the Burst Frequency Offsets (BFOs) associated with automated satellite communications messages received from...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1702.02432
Arxiv.org
by Michael Rosenthal; Wei Wu; Eric Klassen; Anuj Srivastava
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Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in several settings. The model is estimated in a penalized maximum-likelihood framework using gradient-based optimization. Towards that goal, we specify a first-order roughness penalty using the Jacobian of diffeomorphisms. We compare the prediction performance of...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1702.00823
Arxiv.org
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In statistics education, the concept of population is widely felt hard to grasp, as a result of vague explanations in textbooks. Some textbook authors therefore chose not to mention it. This paper offers a new explanation by proposing a new theoretical framework of population and sampling, which aims to achieve high mathematical sensibleness. In the explanation, the term population is given clear definition, and the relationship between simple random sampling and iid random variables are...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1704.01732
Arxiv.org
by Ricardo Almeida
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The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the order of the fractional differential equation that better describes the experimental data, for different types of fractional derivatives.
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1704.00609
Arxiv.org
by Claus Vogl
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In a review on the contribution of J.B.S. Haldane to the development of the Bayes factor hypothesis test (arXiv:1511.08180), Etz and Wagenmakers focus on Haldane's proposition of a mixture prior in a genetic example (Haldane 1932, A note on inverse probability. Mathematical Proceedings of the Cambridge Philosophical Society, 28, 55-61.). As Haldane never followed up on these ideas, it is difficult to gauge his motivation and intentions. I argue that contrary to Haldane's stated intention of...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1702.08261
Arxiv.org
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To many statisticians and citizens, the outcome of the most recent U.S. presidential election represents a failure of data-driven methods on the grandest scale. This impression has led to much debate and discussion about how the election predictions went awry -- Were the polls inaccurate? Were the models wrong? Did we misinterpret the probabilities? -- and how they went right -- Perhaps the analyses were correct even though the predictions were wrong, that's just the nature of probabilistic...
Topics: Other Statistics, Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01171
Arxiv.org
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Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior as well as boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1704.00674
Arxiv.org
by Dave Zachariah; Petre Stoica; Magnus Jansson
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We show that the recently proposed (enhanced) PUMA estimator for array processing minimizes the same criterion function as the well-established MODE estimator. (PUMA = principal-singular-vector utilization for modal analysis, MODE = method of direction estimation.)
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1701.04583
Arxiv.org
by Andrew C. Heusser; Kirsten Ziman; Lucy L. W. Owen; Jeremy R. Manning
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Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable over time as (x,y) coordinates on a graph), it is not always obvious how to visualize high-dimensional datasets in a similarly intuitive way. Here we present HypeTools, a Python toolbox for visualizing and manipulating large, high-dimensional datasets. Our...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1701.08290
Arxiv.org
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Confidence intervals provide a way to determine plausible values for a population parameter. They are omnipresent in research articles involving statistical analyses. Appropriately, a key statistical literacy learning objective is the ability to interpret and understand confidence intervals in a wide range of settings. As instructors, we devote a considerable amount of time and effort to ensure that students master this topic in introductory courses and beyond. Yet, studies continue to find...
Topics: Other Statistics, Statistics
Source: http://arxiv.org/abs/1701.08452
Arxiv.org
by M. Dolores Ruiz-Medina; J. Álvarez-Liébana
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A special class of standard Gaussian Autoregressive Hilbertian processes of order one (Gaussian ARH(1) processes), with bounded linear autocorrelation operator, which does not satisfy the usual Hilbert-Schmidt assumption, is considered. To compensate the slow decay of the diagonal coefficients of the autocorrelation operator, a faster decay velocity of the eigenvalues of the trace autocovariance operator of the innovation process is assumed. As usual, the eigenvectors of the autocovariance...
Topics: Other Statistics, Statistics Theory, Statistics, Applications, Mathematics
Source: http://arxiv.org/abs/1704.05630
Arxiv.org
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Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic properties of simultaneous estimator $\lambda_n(\cdot)$, $\beta_n$ were studied for baseline hazard rate $\lambda(\cdot)$ and regression parameter $\beta$, at that the parameter set $\Theta=\Theta_{\lambda}\times \Theta_{\beta}$ was assumed bounded. In the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.10940
Arxiv.org
by Fadoua Balabdaoui; Cécile Durot; François Koladjo
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Based on the convex least-squares estimator, we propose two different procedures for testing convexity of a probability mass function supported on N with an unknown finite support. The procedures are shown to be asymptotically calibrated.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04367
Arxiv.org
by Sebastian Fuchs; Klaus D. Schmidt
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In the present paper we propose and study estimators for a wide class of bivariate measures of concordance for copulas. These measures of concordance are generated by a copula and generalize Spearman's rho and Gini's gamma. In the case of Spearman's rho and Gini's gamma the estimators turn out to be the usual sample versions of these measures of concordance.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04582
Arxiv.org
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Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. Two recent papers by G\"otze, K\"osters and Tikhomirov (2015) and Zeng (2016) obtain the limit of the empirical spectral distribution for the product when $m$ is a fixed integer. In this paper, we investigate the limiting empirical distribution of scaled...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.06926
Arxiv.org
by Loïc Devilliers; Xavier Pennec; Stéphanie Allassonnière
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We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fr{\'e}chet mean in quotient space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In this...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.01232
Arxiv.org
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Kennedy and O'Hagan (2001) propose a model for calibrating some unknown parameters in a computer model and estimating the discrepancy between the computer output and physical response. This model is known to have certain identifiability issues. Tuo and Wu (2016) show that there are examples for which the Kennedy-O'Hagan method renders unreasonable results in calibration. In spite of its unstable performance in calibration, the Kennedy-O'Hagan approach has a more robust behavior in predicting...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.01326
Arxiv.org
by Johannes Ebert; Vladimir Spokoiny; Alexandra Suvorikova
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In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.03658
Arxiv.org
by Hamzeh Torabi; Sayyed Mahmoud Mirjalili; Hossein Nadeb
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In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for normality is consistent and quite powerful in comparison with existing goodness-of-fit tests based on progressively Type-II censored data. Also, the new test statistic for a real data set is used and the results show that our new test statistic performs...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.06787
Arxiv.org
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The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. The Kullback-Leibler divergences from uniformity of these pdQs are found and interpreted and convergence of the pdQ mapping to the uniform distribution is investigated.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04921
Arxiv.org
by Dragan Radulovic; Marten Wegkamp
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We offer an umbrella type result which extends the convergence of classical empirical process on the line to more general processes indexed by functions of bounded variation. This extension is not contingent on the type of dependence of the underlying sequence of random variables. As a consequence we establish the weak convergence for stationary empirical processes indexed by general classes of functions under alpha mixing conditions.
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.07873
Arxiv.org
by Robert J. Adler; Kevin Bartz; Sam C. Kou; Anthea Monod
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We introduce Lipschitz-Killing curvature (LKC) regression, a new method to produce $(1-\alpha)$ thresholds for signal detection in random fields that does not require knowledge of the spatial correlation structure. The idea is to fit observed empirical Euler characteristics to the Gaussian kinematic formula via generalized least squares, which quickly and easily provides statistical estimates of the LKCs --- complex topological quantities that can be extremely challenging to compute, both...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.08562
Arxiv.org
by Gilles Blanchard; Pierre Neuvial; Etienne Roquain
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We introduce a general methodology for post hoc inference in a large-scale multiple testing framework. The approach is called " user-agnostic " in the sense that the statistical guarantee on the number of correct rejections holds for any set of candidate items selected by the user (after having seen the data). This task is investigated by defining a suitable criterion, named the joint-family-wise-error rate (JER for short). We propose several procedures for controlling the JER, with a...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.02307
Arxiv.org
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
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
Arxiv.org
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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
Arxiv.org
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
Arxiv.org
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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
Arxiv.org
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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
Arxiv.org
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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
Arxiv.org
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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
Arxiv.org
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
Arxiv.org
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
Arxiv.org
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
Arxiv.org
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
Arxiv.org
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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
Arxiv.org
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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
Arxiv.org
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
Arxiv.org
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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
Arxiv.org
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
Arxiv.org
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 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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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
Arxiv.org
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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
Arxiv.org
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
Arxiv.org
by M. A. Abd Elgawad; A. M. Elsawah; Hong Qin; Ting Yan
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In many biological, agricultural, military activity problems and in some quality control problems, it is almost impossible to have a fixed sample size, because some observations are always lost for various reasons. Therefore, the sample size itself is considered frequently to be a random variable (rv). The class of limit distribution functions (df's) of the random bivariate extreme generalized order statistics (GOS) from independent and identically distributed RV's are fully characterized. When...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04682
Arxiv.org
by Sylvie Huet; Marie-Luce Taupin
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We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.04671
We consider the sparse high-dimensional linear regression model $Y=Xb+\epsilon$ where $b$ is a sparse vector. For the Bayesian approach to this problem, many authors have considered the behavior of the posterior distribution when, in truth, $Y=X\beta+\epsilon$ for some given $\beta$. There have been numerous results about the rate at which the posterior distribution concentrates around $\beta$, but few results about the shape of that posterior distribution. We propose a prior distribution for...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.02646
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by Olga Klopp; Nicolas Verzelen
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Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block constant matrices and step function graphons. Surprisingly, our results imply that, from the minimax point of view, the raw data, that is, the adjacency matrix of the observed graph, is already optimal and more involved procedures cannot improve the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.05101
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Lai and Robbins (1985) and Lai (1987) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback-Leibler information of the reward distributions, estimated from within a specified parametric family. In recent years there has been renewed interest in the multi-armed bandit problem due to new applications in machine learning algorithms and data...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.08285
Arxiv.org
by Esmaeil Bashkar; Hamzeh Torabi; Ali Dolati; Felix Belzunce
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In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of this order in the context of stochastic comparison for extreme order statistics of independent samples following the Frechet distribution and scale model. We discuss stochastic comparisons of...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.03656
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This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic distributional properties of the estimators are discussed. A simulation study compares the performance of the minimum distance estimator with other well celebrated estimator. This simulation study shows the superiority of the minimum distance estimator over...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.01199
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by Marie Turčičová; Jan Mandel; Kryštof Eben
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The asymptotic variance of a maximum likelihood estimate is proved to decrease by restricting the maximization to a subspace that is known to contain the true parameter. Covariance matrices of many random fields are known to be diagonal or approximately diagonal in a suitable basis. Such sample covariance matrices were improved by omitting off-diagonal terms. Maximum likelihood estimation on subspaces of diagonal matrices allows a systematic fitting of diagonal covariance models including...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.08185
This paper deals with the estimation problem of misspecified ergodic L\'evy driven stochastic differential equation models based on high-frequency samples. We utilize the widely applicable and tractable Gaussian quasi-likelihood approach which focuses on (conditional) mean and variance struc- ture. It is shown that the corresponding Gaussian quasi-likelihood estimators of drift and scale parameters satisfy tail probability estimates and asymptotic normality at the same rate as correctly...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00908
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by Stéphanie van der Pas; Botond Szabó; Aad van der Vaart
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We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of signals, was known. We drop this assumption and characterize the behavior of the maximum marginal likelihood estimator (MMLE) of a key parameter of the horseshoe prior. We prove that the MMLE is an effective estimator of the sparsity level, in the sense that...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.03698
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by François Roueff; Rainer Von Sachs
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Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracted a lot of interest in applications in the life sciences (seismology, genomics, neuro-science,...), but also in the modelling of high-frequency financial data. In this contribution we provide a fully developed nonparametric estimation theory of both...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.01437
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by Qian Lin; Xinran Li; Dongming Huang; Jun S. Liu
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The central subspace of a pair of random variables $(y,x) \in \mathbb{R}^{p+1}$ is the minimal subspace $\mathcal{S}$ such that $y \perp \hspace{-2mm} \perp x\mid P_{\mathcal{S}}x$. In this paper, we consider the minimax rate of estimating the central space of the multiple index models $y=f(\beta_{1}^{\tau}x,\beta_{2}^{\tau}x,...,\beta_{d}^{\tau}x,\epsilon)$ with at most $s$ active predictors where $x \sim N(0,I_{p})$. We first introduce a large class of models depending on the smallest...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.06009
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by James E. Johndrow; Kristian Lum; David B. Dunson
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There has been substantial recent interest in record linkage, attempting to group the records pertaining to the same entities from a large database lacking unique identifiers. This can be viewed as a type of "microclustering," with few observations per cluster and a very large number of clusters. A variety of methods have been proposed, but there is a lack of literature providing theoretical guarantees on performance. We show that the problem is fundamentally hard from a theoretical...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.04955
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by Zhiqiang Tan; Cun-Hui Zhang
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Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive regression where functional semi-norms are used to induce smoothness of component functions and the empirical $L_2$ norm is used to induce sparsity. The functional semi-norms can be of Sobolev or bounded variation types and are allowed to be different amongst...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.07229
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by Steffen Lauritzen; Alessandro Rinaldo; Kayvan Sadeghi
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We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.08420
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by Yun Yang; Zuofeng Shang; Guang Cheng
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We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax optimality in the asymptotic sense. An important consequence of this non-asymptotic theory is a new and practically useful formula for selecting the optimal smoothing parameter in nonparametric testing. The leading example in this paper is smoothing spline...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.01330
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by Shirshendu Chatterjee; Ofer Zeitouni
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We consider the "searching for a trail in a maze" composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal hypothesis, one observes independent Gaussian variables of unit variance at all nodes, with zero, mean off the anomalous path and mean \mu_n on it. Under the null hypothesis, one observes i.i.d. standard Gaussians on all nodes. Arias-Castro et al....
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.05991
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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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This paper establishes the almost sure convergence and asymptotic normality of levels and differenced quasi maximum-likelihood (QML) estimators of dynamic panel data models. The QML estimators are robust with respect to initial conditions, conditional and time-series heteroskedasticity, and misspecification of the log-likelihood. The paper also provides an ECME algorithm for calculating levels QML estimates. Finally, it uses Monte Carlo experiments to compare the finite sample performance of...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00662
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by Xianyang Zhang; Shun Yao; Xiaofeng Shao
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Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang (2014), and it is able to detect a certain type of departure from the null hypothesis of conditional mean independence without making any specific model assumptions. Theoretically, we establish the asymptotic normality of the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.08697
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by Pierre Alquier; Vincent Cottet; Guillaume Lecué
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We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when $\|\cdot\|$ is any norm, $F$ is a convex class of functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein condition over $F$. We explore both the bounded and subgaussian stochastic frameworks for the distribution of the $f(X_i)$'s, with no...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.01402
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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 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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We show that two estimators, the Square-Root Lasso and the Square-Root Slope can achieve the exact optimal minimax prediction rate, which is $(s/n) \log(p/s)$ in the setting of the sparse high-dimensional linear regression. Here, $n$ is the sample size, $p$ is the dimension and $s$ is the sparsity parameter. We also prove optimality for the estimation error in the $l_q$-norm, with $q \in [1,2]$ for the Square-Root Lasso, and in the $l_2$ and sorted $l_1$ norms for the Square-Root Slope. Both...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.02907
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by A. Philip Dawid; Monica Musio; Silvia Columbu
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We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal likelihood function in such a case, we apply a homogeneous scoring rule. For the particular case of distinguishing between Poisson and Negative Binomial models, we conduct simulations that indicate that, applied prequentially, the method will consistently...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.03353
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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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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 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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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 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
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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 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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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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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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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
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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 Marina Antolín; Eustasio Del Barrio; Jean-Michel Loubes
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Classification rules can be severely affected by the presence of disturbing observations in the training sample. Looking for an optimal classifier with such data may lead to unnecessarily complex rules. So, simpler effective classification rules could be achieved if we relax the goal of fitting a good rule for the whole training sample but only consider a fraction of the data. In this paper we introduce a new method based on trimming to produce classification rules with guaranteed performance...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.05065
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by Gian-Andrea Thanei; Christina Heinze; Nicolai Meinshausen
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Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool in machine learning and statistics. We discuss the applications of random projections in linear regression problems, developed to decrease computational costs, and give an overview of the theoretical guarantees of the generalization error. It can be shown that...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.05325
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by Shih-Hao Huang; Mong-Na Lo Huang; Kerby Shedden; Weng Kee Wong
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We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.00888
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by Yubo Tao; Jun Yu
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This paper examines the limit properties of information criteria (such as AIC, BIC, HQIC) for distinguishing between the unit root model and the various kinds of explosive models. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different order of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.02720
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This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic Nikol'skii classes. We fully characterize the behavior of the minimax risk for different relationships between regularity parameters and norm indexes in the definitions of the functional class and of the risk. In particular, we show that the boundedness of the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.04420
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by Zhipeng Lou; Wei Biao Wu
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Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the truncated sample mean vector. A Gaussian approximation result is derived for the latter under the very mild finite polynomial ($(2+\theta)$-th) moment condition and the dimension $p$ can be allowed to grow exponentially with the sample size $n$. Based on this...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.04806
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by Mehmet Niyazi Cankaya; Olcay Arslan
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The asymmetric objective function is proposed as an alternative to Huber objective function to model skewness and obtain robust estimators for the location, scale and skewness parameters. The robustness and asymptotic properties of the asymmetric M-estimators are explored. A simulation study and real data examples are given to illustrate the performance of proposed asymmetric M-estimation method over the symmetric M-estimation method. It is observed from the simulation results that the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.00378
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Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive computer models by cpu inexpensive mathematical functions, called metamodels. For example, the Gaussian process (Gp) model has shown strong capabilities to solve practical problems , often involving several interlinked issues. However, in case of high...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1704.07090
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by Gilles Blanchard; Alexandra Carpentier; Maurilio Gutzeit
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We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension $d$ and the sample...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.03760
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by Afonso Bandeira; Philippe Rigollet; Jonathan Weed
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This paper describes optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among others. We describe how this model can be viewed as a multivariate Gaussian mixture model under the constraint that the centers belong to the orbit of a group. This enables us to derive matching upper and lower bounds that feature an interesting dependence on the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1702.08546
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by Przemysław Spurek; Jacek Tabor; Przemysław Rola; Michał Ociepka
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Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most of existing methods are based on the minimization of the function of fourth-order moment (kurtosis). Skewness (third-order moment) has received much less attention. In this paper we present a competitive approach to ICA based on the Split Gaussian distribution, which is well adapted to asymmetric data. Consequently, we obtain...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.09160
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by Huong Ha; James S. Welsh; Mazen Alamir
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This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.09344
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It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear combinations in a neighborhood of a simple variability weighted average of these parameters. Surprisingly, this variability weighted average is more accurately estimated when the variables are more strongly correlated, and it is the only linear combination with...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1703.09965
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We consider the Lasso for a noiseless experiment where one has observations $X \beta^0$ and uses the penalized version of basis pursuit. We compute for some special designs the compatibility constant, a quantity closely related to the restricted eigenvalue. We moreover show the dependence of the (penalized) prediction error on this compatibility constant. This exercise illustrates that compatibility is necessarily entering into the bounds for the (penalized) prediction error and that the bounds...
Topics: Statistics Theory, Statistics, Mathematics
Source: http://arxiv.org/abs/1701.03326