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作者：Zhang, Zhixiang; Zheng, Shurong; Pan, Guangming; Zhong, Ping-Shou
作者单位：Nanyang Technological University; Northeast Normal University - China; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are proportional to each other. As a byproduct, we also establish the central limit theorem of the leading sample spiked eigenvalues by removing the block diagonal assumption on the population covariance matrix, which is commonly needed in the literature. Moreover, we pro...
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作者：Chan, Kin Wai
作者单位：Chinese University of Hong Kong
摘要：Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or suboptimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many exis...
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作者：Yang, Wenhao; Zhang, Liangyu; Zhang, Zhihua
作者单位：Peking University; Peking University
摘要：In this paper, we study the nonasymptotic and asymptotic performances of the optimal robust policy and value function of robust Markov Decision Processes (MDPs), where the optimal robust policy and value function are estimated from a generative model. While prior work focusing on nonasymptotic performances of robust MDPs is restricted in the setting of the KL uncertainty set and (s, a)-rectangular assumption, we improve their results and also consider other uncertainty sets, including the L-1 ...
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作者：Feng, Huijie; Ning, Yang; Zhao, Jiwei
作者单位：Cornell University; University of Wisconsin System; University of Wisconsin Madison
摘要：Given a large number of covariates Z, we consider the estimation of a high-dimensional parameter theta in an individualized linear threshold theta(T) Z for a continuous variable X, which minimizes the disagreement between sign(X - theta(T) Z) and a binary response Y. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating theta even in...
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作者：Ndaoud, Mohamed
作者单位：ESSEC Business School
摘要：In this paper, we study the problem of clustering in the Two component Gaussian mixture model when the centers are separated by some Delta > 0. We present a nonasymptotic lower bound for the corresponding minimax Hamming risk improving on existing results. We also propose an optimal, efficient and adaptive procedure that is minimax rate optimal. The rate optimality is moreover sharp in the asymptotics when the sample size goes to infinity. Our procedure is based on a variant of Lloyd's iterati...
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作者：He, Yuanzhen; Lin, C. Devon; Sun, Fasheng
作者单位：Beijing Normal University; Queens University - Canada; Northeast Normal University - China; Northeast Normal University - China
摘要：Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative and quantitative factors, multiple computer experiments, multifidelity computer experiments, cross-validation and stochastic optimization, orthogonal arrays with certain structures have been introduced. Sliced orthogonal arrays and nested orthogonal arrays a...
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作者：Chan, Kin Wai
作者单位：Chinese University of Hong Kong
摘要：Multiple imputation (MI) is a technique especially designed for handling missing data in public-use datasets. It allows analysts to perform incompletedata inference straightforwardly by using several already imputed datasets released by the dataset owners. However, the existing MI tests require either a restrictive assumption on the missing-data mechanism, known as equal odds of missing information (EOMI), or an infinite number of imputations. Some of them also require analysts to have access ...
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作者：Zhang, Yuan; Xia, Dong
作者单位：University System of Ohio; Ohio State University; Hong Kong University of Science & Technology
摘要：Network method of moments (Ann. Statist. 39 (2011) 2280-2301) is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this paper, we present the first higher-order accurate approximation to the sampling CDF of a studentized network moment by Edgeworth expansion. In sharp contrast to classical literature on noiseless U-statistics, we show that the Edgeworth expa...
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作者：Durre, Alexander; Paindaveine, Davy
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We consider the fundamental problem of estimating the location of a d-variate probability measure under an L-p loss function. The naive estimator, that minimizes the usual empirical L-p risk, has a known asymptotic behavior but suffers from several deficiencies for p not equal 2, the most important one being the lack of equivariance under general affine transformations. In this work, we introduce a collection of L-p location estimators (mu) over cap (p,l)(n) that minimize the size of suitable ...
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作者：Fathi, Max; Goldstein, Larry; Reinert, Gesine; Saumard, Adrien
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; University of Southern California; University of Oxford; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Universite de Rennes
摘要：Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein's Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the G...
