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作者：Clemencon, Stephan; Lugosi, Gabor; Vayatis, Nicolas
作者单位：Universite Paris Nanterre; ICREA; Pompeu Fabra University; Pompeu Fabra University; Universite Paris Cite; Sorbonne Universite
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作者：Donoho, David; Jin, Jiashun
作者单位：Stanford University; Purdue University System; Purdue University
摘要：We apply FDR thresholding to a non-Gaussian vector whose coordinates X-i, i = 1,..., n, are independent exponential with individual means mu(i). The vector mu = (mu(i)) is thought to be sparse, with most coordinates 1 but a small fraction significantly larger than 1; roughly, most coordinates are simply 'noise,' but a small fraction contain 'signal.' We measure risk by percoordinate mean-squared error in recovering log(mu(i)), and study minimax estimation over parameter spaces defined by const...
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作者：van de Geer, Sara
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
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作者：Bartlett, Peter L.; Mendelson, Shahar
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Australian National University
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作者：Blanchard, Gilles; Massart, Pascal
作者单位：Fraunhofer Gesellschaft; Fraunhofer Germany; Fraunhofer Institute Center Schloss Birlinghoven; Universite Paris Saclay
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作者：Zu, Yijun; He, Xuming
作者单位：Michigan State University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer Statist. Assoc. 88 (1993) 252-260]. The present paper proves the conjecture under general regula...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology; University of New Mexico
摘要：Let F be a class of measurable functions f : S -> [0, 1] defined on a probability space (S, A, P). Given a sample (X-1,X-...,X- X-n) of i.i.d. random variables taking values in S with common distribution P, let P-n denote the empirical measure based on (X-1,X-...,X- X-n). We study an empirical risk minimization problem P-n f -> min, f is an element of F. Given a solution (f) over cap (n) of this problem, the goal is to obtain very general upper bounds on its excess risk E-p((f) over cap (n)) ;...
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作者：Hallin, Marc; Paindaveine, Davy
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We propose a class of rank-based procedures for testing that the shape matrix V of an elliptical distribution (with unspecified center of symmetry, scale and radial density) has some fixed value V-0; this includes, for V-0 = I-k, the problem of testing for sphericity as an important particular case. The proposed tests are invariant under translations, monotone radial transformations, rotations and reflections with respect to the estimated center of symmetry. They are valid without any moment a...
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作者：Tsybakov, A. B.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
