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作者：Chen, Xiaohui
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper studies the Gaussian and bootstrap approximations for the probabilities of a nondegenerate U-statistic belonging to the hyperrectangles in R-d when the dimension d is large. A two-step Gaussian approximation procedure that does not impose structural assumptions on the data distribution is proposed. Subject to mild moment conditions on the kernel, we establish the explicit rate of convergence uniformly in the class of all hyperrectangles in Rd that decays polynomially in sample size ...
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作者：Bellec, Pierre C.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Rutgers University System; Rutgers University New Brunswick; Institut Polytechnique de Paris; ENSAE Paris
摘要：The performance of Least Squares (LS) estimators is studied in shape-constrained regression models under Gaussian and sub-Gaussian noise. General bounds on the performance of LS estimators over closed convex sets are provided. These results have the form of sharp oracle inequalities that account for the model misspecification error. In the presence of misspecification, these bounds imply that the LS estimator estimates the projection of the true parameter at the same rate as in the well-specif...
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作者：Lin, Qian; Zhao, Zhigen; Liu, Jun S.
作者单位：Tsinghua University; Harvard University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]. Under mild conditions, the asymptotic ratio rho = lim p/n is the phase transition parameter and the SIR estimator is consistent if and only if rho = 0. When dimension p is greater than n, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with ...
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作者：Kaufmann, Emilie
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite de Lille; Centrale Lille
摘要：This paper is about index policies for minimizing (frequentist) regret in a stochastic multi-armed bandit model, inspired by a Bayesian view on the problem. Our main contribution is to prove that the Bayes-UCB algorithm, which relies on quantiles of posterior distributions, is asymptotically optimal when the reward distributions belong to a one-dimensional exponential family, for a large class of prior distributions. We also show that the Bayesian literature gives new insight on what kind of e...
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作者：Fan, Jianqing; Liu, Han; Sun, Qiang; Zhang, Tong
作者单位：Fudan University; Princeton University; Princeton University; University of Toronto
摘要：We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high-dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second...
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作者：Behr, Merle; Holmes, Chris; Munk, Axel
作者单位：University of Gottingen; University of Oxford; Max Planck Society
摘要：We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an epsilon-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and ...
