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作者：Kneip, Alois; Sarda, Pascal
作者单位：University of Bonn; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach: it is assumed that the predictor vector can be decomposed into a sum of two uncorrelated random components reflecting common factors and specific variabilities of the explanatory variables. It is shown that the traditional assumpt...
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作者：Maruyama, Yuzo; George, Edward I.
作者单位：University of Tokyo; University of Pennsylvania
摘要：For the normal linear model variable selection problem, we propose selection criteria based on a fully Bayes formulation with a generalization of Zellner's g-prior which allows for p > n. A special case of the prior formulation is seen to yield tractable closed forms for marginal densities and Bayes factors which reveal new model evaluation characteristics of potential interest.
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作者：Arias-Castro, Ery; Candes, Emmanuel J.; Plan, Yaniv
作者单位：University of California System; University of California San Diego; Stanford University; California Institute of Technology
摘要：Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon the order of p(1-alpha) of those, 0 <= alpha <= 1. Under ...
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作者：Khare, Kshitij; Hobert, James P.
作者单位：State University System of Florida; University of Florida
摘要：The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo algorithm that is easy to implement but often suffers from slow convergence. The sandwich algorithm is an alternative that can converge much faster while requiring roughly the same computational effort per iteration. Theoretically, the sandwich algorithm always converges at least as fast as the corresponding DA algorithm in the sense that parallel to K*parallel to <= parallel to K parallel to, where K and K* are the...
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作者：Cai, T. Tony; Yuan, Ming
作者单位：University of Pennsylvania; University System of Georgia; Georgia Institute of Technology
摘要：The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs. Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced. The analysis reveals interesting and different phase transition phenomena in the two cases. Under the common design, the sampling frequency solely ...
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作者：Lai, Tze Leung; Gross, Shulamith T.; Shen, David Bo
作者单位：Stanford University; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used to assess the efficacy of the forecast probabilities after observing the occurrence, or nonoccurrence, of the predicted events. We develop herein a statistical theory for scoring rules and propose an alternative approach to the evaluation of probability fore...
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作者：Chu, Tingjin; Zhu, Jun; Wang, Haonan
作者单位：Colorado State University System; Colorado State University Fort Collins; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the problem of selecting covariates ill spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and, for ease of computation, PMLE is approximated by one-step sparse estimation (OSE). To further improve computational efficiency, particularly with large sample sizes, we propose penalized maximum covariance-tapered likelihood estimation (PMLET) and its one-ste...
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作者：Bontemps, Dominique
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：This paper brings a contribution to the Bayesian theory of nonparametric and semiparametric estimation. We are interested in the asymptotic normality of the posterior distribution in Gaussian linear regression models when the number of regressors increases with the sample size. Two kinds of Bernstein-von Mises theorems are obtained in this framework: nonparametric theorems for the parameter itself, and semiparametric theorems for functionals of the parameter. We apply them to the Gaussian sequ...
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作者：Koltchinskii, Vladimir; Lounici, Karim; Tsybakov, Alexandre B.
作者单位：University System of Georgia; Georgia Institute of Technology; Institut Polytechnique de Paris; ENSAE Paris
摘要：This paper deals with the trace regression model where n entries or linear combinations of entries of an unknown m(1) x m(2) matrix A(0) corrupted by noise are observed. We propose a new nuclear-norm penalized estimator of A(0) and establish a general sharp oracle inequality for this estimator for arbitrary values of n, m(1), m(2) under the condition of isometry in expectation. Then this method is applied to the matrix completion problem. In this case, the estimator admits a simple explicit fo...
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作者：Hoffmann, Marc; Nickl, Richard
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Cambridge
摘要：The problem of existence of adaptive confidence bands for an unknown density f that belongs to a nested scale of Holder classes over R or [0, 1] is considered. Whereas honest adaptive inference in this problem is impossible already for a pair of Holder balls Sigma (r), Sigma(s), r not equal s, of fixed radius, a non-parametric distinguishability condition is introduced under which adaptive confidence bands can be shown to exist. It is further shown that this condition is necessary and sufficie...
