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作者：Cai, T. Tony; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax lower bound. The problem exhibits new features that are significantly different from those that occur in the conventional nonparametric function estimation problems. Standard techniques fail to yield good results, and new tools are thus needed. We first develo...
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作者：Zhu, Hongtu; Li, Runze; Kong, Linglong
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Alberta
摘要：Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then...
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作者：Neuvial, Pierre; Roquain, Etienne
作者单位：INRAE; Universite Paris Saclay; Universite Paris Cite; Sorbonne Universite
摘要：We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The 0-class (null) is assumed to have a known density while the 1-class (alternative) is obtained from the 0-class either by translation or by scaling. Furthermore, the 1-class is assumed to have a small number of elements w.r.t. the 0-class (sparsity). We focus on densities of the Subbotin family, including Gaussian and Laplace models. Nonasymptotic oracle inequalities are derived for the...
