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作者：Candes, Emmanuel J.; Soltanolkotabi, Mahdi
作者单位：Stanford University
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作者：Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S.
作者单位：California Institute of Technology; Massachusetts Institute of Technology (MIT)
摘要：Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of latent components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in which the latent and observed variables are jointly Gaussian, with the conditional statistics of the o...
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作者：Portnoy, Stephen
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Traditionally, assessing the accuracy of inference based on regression quantiles has relied on the Bahadur representation. This provides an error of order n(-1/4) in normal approximations, and suggests that inference based on regression quantiles may not be as reliable as that based on other (smoother) approaches, whose errors are generally of order n(-1/2) (or better in special symmetric cases). Fortunately, extensive simulations and empirical applications show that inference for regression q...
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作者：Rivoirard, Vincent; Rousseau, Judith
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：In this paper, we study the asymptotic posterior distribution of linear functionals of the density by deriving general conditions to obtain a semiparametric version of the Bernstein-von Mises theorem. The special case of the cumulative distributive function, evaluated at a specific point, is widely considered. In particular, we show that for infinite-dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional can be either Gaussian...
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作者：Bunea, Florentina; She, Yiyuan; Wegkamp, Marten H.
作者单位：Cornell University; State University System of Florida; Florida State University; Cornell University
摘要：We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-dimensional approximations of the parameter matrix in such models. We show in this article that important gains in prediction accuracy can be obtained by considering them jointly....
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作者：Castillo, Ismael; van der Vaart, Aad
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Vrije Universiteit Amsterdam
摘要：We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero means and next a prior on the nonzero values. We consider the posterior distribution in the frequentist set-up that the observations are generated according to a fixed mean vector, and are interested in the posterior distribution of the number of nonzero co...
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作者：Bayarri, M. J.; Berger, J. O.; Forte, A.; Garcia-Donato, G.
作者单位：University of Valencia; Duke University; Universitat Jaume I; Universidad de Castilla-La Mancha
摘要：In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the ...
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作者：Shao, Jun; Deng, Xinwei
作者单位：East China Normal University; University of Wisconsin System; University of Wisconsin Madison; Virginia Polytechnic Institute & State University
摘要：Because of the advance in technologies, modem statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems with deterministic design points is very different from those in the case of random covariates, due to the identifiability of the high-dimensional regression parameter vector. We show that a reasonable approach is to focus on the projection of the regression...
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作者：Bai, Jushan; Li, Kunpeng
作者单位：Columbia University; Tsinghua University; University of International Business & Economics; Central University of Finance & Economics
摘要：This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlik...
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作者：Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S.
作者单位：California Institute of Technology; Massachusetts Institute of Technology (MIT)
