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18

Jun 25, 2018
06/18

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Bikramjit Das; Souvik Ghosh

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In many practical situations exploratory plots are helpful in understanding tail behavior of sample data. The Mean Excess plot is often applied in practice to understand the right tail behavior of a data set. It is known that if the underlying distribution of a data sample is in the domain of attraction of a Frechet, Gumbel or Weibull distributions then the ME plot of the data tend to a straight line in an appropriate sense, with positive, zero or negative slopes respectively. In this paper we...

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00518

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13

Jun 25, 2018
06/18

by
Mansi Garg; Isha Dewan

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Let ${X_n, n \ge 1}$ be a sequence of stationary associated random variables. For such a sequence, we discuss the limiting behavior of U-statistics based on kernels which are of bounded Hardy-Krause variation.

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00868

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18

Jun 25, 2018
06/18

by
Leonid Torgovitski

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We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even...

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00177

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13

Jun 25, 2018
06/18

by
Vygantas Paulauskas; Marijus Vaičiulis

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In the paper we propose some new class of functions which is used to construct tail index estimators. Functions from this new class is non-monotone in general, but presents a product of two monotone functions: the power function and the logarithmic function, which plays essential role in the classical Hill estimator. Introduced new estimators have better asymptotic performance comparing with the Hill estimator and other popular estimators over all range of the parameters present in the second...

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00811

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22

Jun 25, 2018
06/18

by
Emilie Devijver

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We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We consider predictor selection and rank reduction to obtain lower-dimensional approximations. A class of estimators with a fast rate of convergence is introduced. We apply this result to a specific procedure, introduced in [11], where the relevant predictors are...

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00442

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14

Jun 25, 2018
06/18

by
Viktoria Öllerer; Christophe Croux; Andreas Alfons

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To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the...

Topics: Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.01208

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Jun 25, 2018
06/18

by
Anders Bredahl Kock; Haihan Tang

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We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities are derived for the fixed effects. Next, we show how one can conduct uniformly valid simultaneous inference on the parameters of the model and construct a uniformly valid estimator of the asymptotic covariance matrix which is robust to conditional...

Topics: Statistics Theory, Mathematics, Methodology, Statistics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00478

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Jun 25, 2018
06/18

by
Akihiko Inoue; Yukio Kasahara; Mohsen Pourahmadi

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We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral characterizations for this property from univariate processes to multivariate processes.

Topics: Probability, Mathematics, Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00625

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15

Jun 25, 2018
06/18

by
Ning Hao; Yang Feng; Hao Helen Zhang

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Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects and interaction effects. Existing regularization methods generally achieve this goal by solving complex optimization problems, which usually demands high computational cost and hence are not feasible for high dimensional data. This paper focuses on scalable...

Topics: Methodology, Statistics, Statistics Theory, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00049

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Jun 25, 2018
06/18

by
Muhyiddin Izadi; Baha-Eldin Khaledi; Chin-Diew Lai

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Suppose F and G are two life distribution functions. It is said that F is more IFRA than G (written by F

Topics: Statistics Theory, Mathematics, Other Statistics, Statistics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.00599

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Jun 28, 2018
06/18

by
Jinzhu Li; Qihe Tang

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Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting from investments. Its wealth process is described in a standard discrete-time model in which, during each period, the insurance risk is quantified as a real-valued random variable $X$ equal to the total amount of claims less premiums, and the financial risk as a...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1507.07673

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Jun 26, 2018
06/18

by
Michele Pavon

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It is observed that for testing between simple hypotheses where the cost of Type I and Type II errors can be quantified, it is better to let the optimization choose the test size.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1502.01328

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7.0

Jun 30, 2018
06/18

by
Prithwish Bhaumik; Subhashis Ghosal

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Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which have to be estimated from the noisy data. Often there is no closed form analytic solution of the equations and hence we cannot use the usual non-linear least squares technique to estimate the unknown parameters. There is a two step approach to solve this...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.0609

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Jun 30, 2018
06/18

by
Serguei Dachian; Yury Kutoyants; Lin Yang

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We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test, of the General Likelihood Ratio test, of the Wald test and of two Bayes tests in the situation when the intensity function of the observed inhomogeneous Poisson process is smooth with respect to the parameter. It is shown that almost all these tests are...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.7867

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5.0

Jun 30, 2018
06/18

by
Zheng Fang; Andres Santos

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This paper studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings, the asymptotic distribution of the plug-in estimator $\phi(\hat \theta_n)$ can be readily derived employing existing extensions to the Delta method. We show, however, that the "standard" bootstrap is only consistent under overly stringent...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1404.3763

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4.0

Jun 30, 2018
06/18

by
Lisandro Fermín; Ricardo Ríos; Luis-Angel Rodríguez

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We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression function in each regime using a Nadaraya-Watson type estimator. Second, we introduce a nonparametric recursive algorithm in the case of hidden Markov switching regime. Our algorithm restores the missing data by means of a Monte-Carlo step and estimate the...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1407.3747

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7.0

Jun 30, 2018
06/18

by
Senthil B. Girimurugan; Eric Chicken

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Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard thresholding. The proposed analytic distribution is made feasible only due to the assumption of normality. Since the statistic is developed for applications in high dimensional data analysis, the assumption holds true in most practical situations. In the...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1408.2581

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16

Jun 26, 2018
06/18

by
Jan Johannes; Anna Simoni; Rudolf Schenk

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In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data. While this establishes posterior consistency, however, the concentration rate depends on both $\theta^\circ$ and a tuning parameter which enters the prior distribution. We first provide an oracle optimal choice of the tuning parameter, i.e., optimized for each...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1502.00184

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18

Jun 28, 2018
06/18

by
Botond Szabó; A. W. van der Vaart; J. H. van Zanten

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Rejoinder of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1509.01906

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6.0

Jun 29, 2018
06/18

by
Tri Le; Bertrand Clarke

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In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model averaging procedure that gives a composite predictor by combining individual predictors from a list of models using weights that optimize a cross-validation criterion. We show that the stacking weights also asymptotically minimize a posterior expected loss. Hence we...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1602.05162

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4.0

Jun 29, 2018
06/18

by
Xianchao Xie; S. C. Kou; Lawrence Brown

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This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semiparametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1603.09144

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7.0

Jun 29, 2018
06/18

by
Rajarshi Mukherjee; Eric Tchetgen Tchetgen; James Robins

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We provide general adaptive upper bounds for estimators of nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models using projection type kernels. An accompanying general adaptive lower bound tool is provided yielding bounds on chi-square divergence between mixtures of product measures. We then provide examples of functionals for which the theory produces rate optimally matching adaptive upper and lower bound.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1608.01364

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5.0

Jun 30, 2018
06/18

by
Dana Yang

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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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18

Jun 27, 2018
06/18

by
Azzouz Dermoune Daoud Ounaissi Nadji Rahmania

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We show that Lasso and Bayesian Lasso are very close when the sparsity is large and the noise is small. Then we propose to solve Bayesian Lasso using multivalued stochastic differential equation. We obtain three discretizations algorithms, and propose a method for calculating the cost of Monte-Carlo (MC), multilevel Monte Carlo (MLMC) and MCMC algorithms.

Topics: Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1504.06441

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Jun 27, 2018
06/18

by
Yang Feng; Yuguo Chen; Xuming He

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Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around asymptotic theories and efficient algorithms. However, not much work has been published under the Bayesian framework. One challenging problem for Bayesian quantile regression is that the full likelihood has no parametric forms. In this paper, we propose a...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1506.00834

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Jun 28, 2018
06/18

by
Daniel J. Graham; Emma J. McCoy; David A. Stephens

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This paper constructs a doubly robust estimator for continuous dose-response estimation. An outcome regression model is augmented with a set of inverse generalized propensity score covariates to correct for potential misspecification bias. From the augmented model we can obtain consistent estimates of mean average potential outcomes for distinct strata of the treatment. A polynomial regression is then fitted to these point estimates to derive a Taylor approximation to the continuous...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1506.04991

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11

Jun 28, 2018
06/18

by
Elvira Di Nardo

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In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical umbral calculus, as introduced by Rota and Taylor in $1994.$ The usefulness of this symbolic technique is twofold. The first is to show how new algebraic identities drive in discovering insights among topics apparently very far from each other and related to...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1512.08379

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6.0

Jun 29, 2018
06/18

by
Victor-Emmanuel Brunel

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Tukey depth, aka halfspace depth, has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample, we investigate the concentration of upper level sets of the Tukey depth relative to that sample around their population version. We also study the concentration of the upper level sets of a discretized version of Tukey depth.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1605.09456

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8.0

Jun 29, 2018
06/18

by
Arturo Erdely

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A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1610.00780

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Jun 30, 2018
06/18

by
Mengyu Xu; Danna Zhang; Wei Biao Wu

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We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample size $n$ and the moment condition. Under proper normalization, central and non-central limit theorems are obtained. To facilitate the related statistical inference, we propose a plug-in calibration method and a re-sampling procedure to approximate the...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1405.7244

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6.0

Jun 30, 2018
06/18

by
Hitoshi Koyano; Morihiro Hayashida; Tatsuya Akutsu

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In this study, we address the problem of clustering string data in an unsupervised manner by developing a theory of a mixture model and an EM algorithm for string data based on probability theory on a topological monoid of strings developed in our previous studies. We first construct a parametric distribution on a set of strings in the motif of the Laplace distribution on a set of real numbers and reveal its basic properties. This Laplace-like distribution has two parameters: a string that...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1411.6471

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12

Jun 27, 2018
06/18

by
Wolf-Dieter Richter

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First and second kind modifications of usual confidence intervals for estimating the expectation and of usual local alternative parameter choices are introduced in a way such that the asymptotic behavior of the true non-covering probabilities and the covering probabilities under the modified local non-true parameter assumption can be asymptotically exactly controlled. The orders of convergence to zero of both types of probabilities are assumed to be suitably bounded below according to an...

Topics: Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1504.02553

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5.0

Jun 29, 2018
06/18

by
Alejandra Cabaña; Ana Maria Estrada; Jairo I. Peña; Adolfo J. Quiroz

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Three different permutation test schemes are discussed and compared in the context of the two-sample problem for functional data. One of the procedures was essentially introduced by Lopez-Pintado and Romo (2009), using notions of functional data depth to adapt the ideas originally proposed by Liu and Singh (1993) for multivariate data. Of the new methods introduced here, one is also based on functional data depths, but uses a different way (inspired by Meta-Analysis) to assess the significance...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1610.06960

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6.0

Jun 29, 2018
06/18

by
Samuel Rosa

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When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for estimating this set of functions of interest. Also, given a weighted eigenvalue-based criterion, we construct a system of estimable functions, so that the optimality for estimating this system of functions is equivalent to the weighted optimality....

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1610.06427

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6.0

Jun 30, 2018
06/18

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

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5.0

Jun 30, 2018
06/18

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

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Jun 28, 2018
06/18

by
Subhashis Ghosal

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Discussion of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1509.01905

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14

Jun 28, 2018
06/18

by
Herold Dehling; Brice Franke; Jeannette H. C. Woerner

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We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast to the classical fractional Ornstein Uhlenbeck process without periodic mean function the rate of convergence is slower depending on the Hurst parameter $H$, namely $n^{1-H}$.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1509.03163

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4.0

Jun 28, 2018
06/18

by
Shaun Fallat; Steffen Lauritzen; Kayvan Sadeghi; Caroline Uhler; Nanny Wermuth; Piotr Zwiernik

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We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semigraphoid which is upward-stable and singleton-transitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1510.01290

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3.0

Jun 28, 2018
06/18

by
Xiaolei Lu; Satoshi Kuriki

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We propose simultaneous confidence bands of the hyperbolic-type for the contrasts between several nonlinear (curvilinear) regression curves. The critical value of a confidence band is determined from the distribution of the maximum of a chi-square random process defined on the domain of explanatory variables. We use the volume-of-tube method to derive an upper tail probability formula of the maximum of a chi-square random process, which is asymptotically exact and sufficiently accurate in...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1510.05077

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4.0

Jun 28, 2018
06/18

by
Jason Leung

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We consider the problem of estimating the s-th derivative of a density function f by the tilted Kernel estimator introduced in Hall and Doosti (2012). Then we further show this estimator achieves the same convergence rate, in probability, the wavelet estimators achieved as shown in Hall and Patil (1995).

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1510.07789

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4.0

Jun 28, 2018
06/18

by
Teppei Ogihara; Nakahiro Yoshida

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We introduce a point process regression model that is applicable to price models and limit order book models. Hawkes type autoregression in the intensity process is generalized to a stochastic regression to covariate processes. We establish the so-called quasi likelihood analysis, which gives a polynomial type large deviation estimate for the statistical random field. We derive large sample properties of the maximum likelihood type estimator and the Bayesian type estimator when the intensity...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1512.01619

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6.0

Jun 29, 2018
06/18

by
Louiza Soltane; Djamel Meraghni; Abdelhakim Necir

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Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when the risks are randomly right-censored. The asymptotic normality of the proposed estimator is established under suitable conditions and its performance evaluated through sets of simulated data.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1602.02605

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4.0

Jun 29, 2018
06/18

by
Holger Dette; Andrey Pepelyshev; Anatoly Zhigljavsky

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In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples. The resulting procedure (estimator and design) provides nearly the same efficiency as the weighted...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1602.03794

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3.0

Jun 29, 2018
06/18

by
Alexei Onatski; Chen Wang

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Johansen's (1988, 1991) likelihood ratio test for cointegration rank of a Gaussian VAR depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the distribution almost surely weakly...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1605.08880

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Jun 28, 2018
06/18

by
Michael J. Lew

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The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability, domination of all other hypotheses by the uninteresting, determinist hypothesis that whatever happened had to happen. Such examples are generally assumed to be important obstacles to the application of the likelihood principle: they are counter-examples to the...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1507.08394

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4.0

Jun 28, 2018
06/18

by
Weihua Deng; Wanli Wang; Xinchun Tian; Yujiang Wu

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In the renewal processes, if the waiting time probability density function is a tempered power-law distribution, then the process displays a transition dynamics; and the transition time depends on the parameter $\lambda$ of the exponential cutoff. In this paper, we discuss the aging effects of the renewal process with the tempered power-law waiting time distribution. By using the aging renewal theory, the $p$-th moment of the number of renewal events $n_a(t_a, t)$ in the interval $(t_a, t_a+t)$...

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1511.06540

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Jun 29, 2018
06/18

by
Alexander Petersen; Hans-Georg Müller

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Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used Hilbert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hilbert space of functions through a continuous and...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1601.02869

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Jun 29, 2018
06/18

by
Jiang Hu; Zhidong Bai

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In this paper, we will introduce the so called naive tests and give a brief review on the newly development. Naive testing methods are easy to understand and performs robust especially when the dimension is large. In this paper, we mainly focus on reviewing some naive testing methods for the mean vectors and covariance matrices of high dimensional populations and believe this naive test idea can be wildly used in many other testing problems.

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1603.01003

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5.0

Jun 29, 2018
06/18

by
Trisha Maitra; Sourabh Bhattacharya

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Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is modeled by a random effect times a known function free of parameters. The distribution of the random effects are assumed to depend upon unknown parameters which are to be learned about. Assuming the independent and identical (iid) situation the authors provide independent proofs of consistency and asymptotic normality of the maximum likelihood estimators (MLEs) of the...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1605.03330