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作者：Coram, Marc; Lalley, Steven P.
作者单位：University of Chicago
摘要：do nonparametric Bayesian procedures overfit? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let v be any probability distribution on the nonnegative integers. To sample a function f from the prior pi(v), first sample m from v and then sample f uniformly from the set of step functions from [0,...
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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：Romano, Joseph P.; Shaikh, Azeem M.
作者单位：Stanford University; Stanford University
摘要：Consider the multiple testing problem of testing null hypotheses H-1,..., H-S. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. But if s is large, control of the FWER is so stringent that the ability of a procedure that controls the FWER to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. T...
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作者：Wei, Ying; He, Xuming
作者单位：Columbia University; University of Illinois System; University of Illinois Urbana-Champaign
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作者：Goldenshluger, Alexander; Zeevi, Assaf
作者单位：University of Haifa; Columbia University
摘要：We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane ...
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作者：Abramovich, Felix; Benjamini, Yoav; Donoho, David L.; Johnstone, Iain M.
作者单位：Tel Aviv University; Stanford University
摘要：We attempt to recover an n-dimensional vector observed in white noise, where n is large and the vector is known to be sparse, but the degree of sparsity is unknown. We consider three different ways of defining sparsity of a vector: using the fraction of nonzero terms; imposing power-law decay bounds on the ordered entries; and controlling the l(p) norm for p small. We obtain a procedure which is asymptotically minimax for l(r) loss, simultaneously throughout a range of such sparsity classes. T...
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作者：Dupuy, Jean-Francois; Grama, Ion; Mesbah, Mounir
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Sorbonne Universite
摘要：The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A frequent problem, however, is the occurence of missing covariate data. A recent approach to estimation in the Cox model in this case jointly models survival and the longitudinal covariate. However, theoretical justification of this approach is still lacking. In ...
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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：Zuo, Yijun
作者单位：Michigan State University
摘要：As estimators of location parameters, univariate trimmed means are well known for their robustness and efficiency. They can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy-tailed models. This paper introduces multidimensional trimmed means based on projection depth induced regions. Robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point. The influence function capt...
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作者：Cavalier, L.; Golubev, Yu.
作者单位：Aix-Marseille Universite
摘要：We study a standard method of regularization by projections of the linear inverse problem Y = Af + epsilon, where epsilon is a white Gaussian noise, and A is a known compact operator with singular values converging to zero with polynomial decay. The unknown function f is recovered by a projection method using the singular value decomposition of A. The bandwidth choice of this projection regularization is governed by a data-driven procedure which is based on the principle of risk hull minimizat...
