The Annals of Statistics

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• Rates of contraction of posterior distributions based on Gaussian process priors AI翻译
  作者：Van Der Wart, A. W.; Van Zanten, J. H.
  作者单位：Vrije Universiteit Amsterdam
  摘要：We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing kernel Hilbert space of the Gaussian process and the small ball probabilities of the Gaussian process. We determine these quantities for a range of examples of Gaussian priors and in several statistical settings. For instance, we consider the rate of contracti...
• LEARNING BY MIRROR AVERAGING AI翻译
  作者：Juditsky, A.; Rigollet, P.; Tsybakov, A. B.
  作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris
  摘要：Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We...
• The distribution of maxima of approximately Gaussian random fields AI翻译
  作者：Nardi, Yuval; Siegmund, David O.; Yakir, Benjamin
  作者单位：Carnegie Mellon University; Stanford University; Hebrew University of Jerusalem
  摘要：Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown location (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The method is based on an application of a likelihood-ratio-identity followed by approximations of local fie...
• Variable selection in semiparametric regression modeling AI翻译
  作者：Li, Runze; Liang, Hua
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Rochester
  摘要：In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures includ...
• ROBUST NONPARAMETRIC ESTIMATION VIA WAVELET MEDIAN REGRESSION AI翻译
  作者：Brown, Lawrence D.; Cai, T. Tony; Zhou, Harrison H.
  作者单位：University of Pennsylvania; Yale University
  摘要：In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are heavy-tailed, and may not even possess variances or means. Our approach is to first use local medians to turn the problem of nonparametric regression with unknown noise distribution into a standard Gaussian regression problem and then apply a wavelet block ...
• CHOICE OF NEIGHBOR ORDER IN NEAREST-NEIGHBOR CLASSIFICATION AI翻译
  作者：Hall, Peter; Park, Byeong U.; Samworth, Richard J.
  作者单位：University of Melbourne; Seoul National University (SNU); University of Cambridge
  摘要：The kth-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of k; and by the absence of techniques for empirical choice of k. In the present paper we detail the way in which the value of k determines the misclassification error. We consider two models, Poisson and Bino...
• Asymptotic equivalence for nonparametric regression with multivariate and random design AI翻译
  作者：Reiss, Markus
  作者单位：Ruprecht Karls University Heidelberg
  摘要：We show that nonparametric regression is asymptotically equivalent, in Le Cam's sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random design.
• Current status data with competing risks: Consistency and rates of convergence of the MLE AI翻译
  作者：Groeneboom, Piet; Maathuis, Marloes H.; Wellner, Jon A.
  作者单位：Delft University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle; Vrije Universiteit Amsterdam
  摘要：We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler naive estimator. Both types of estimators were studied by Jewell, van der Laan and Henneman [Biometrika (2003) 90 183-197], but little was known about their large sample properties. We have started to fill this gap, by proving that the estimators are consisten...
• A theoretical comparison of the data augmentation, marginal augmentation and PX-DA algorithms AI翻译
  作者：Hobert, James P.; Marchev, Dobrin
  作者单位：State University System of Florida; University of Florida; City University of New York (CUNY) System; Baruch College (CUNY); City University of New York (CUNY) System; Baruch College (CUNY)
  摘要：The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo (MCMC) algorithm that is based on a Markov transition density of the form p(x vertical bar x') = integral y fx vertical bar y (x vertical bar y)fY vertical bar X (y vertical bar x') dy, where fX vertical bar Y and fY vertical bar X are conditional densities. The PX-DA and marginal augmentation algorithms of Liu and Wu [J. Amer. Statist. Assoc. 94 (1999) 1264-1274] and Meng and van Dyk [Biometrika 86 (1999) 301-320] ...
• High-dimensional generalized linear models and the lasso AI翻译
  作者：van de Geer, Sara A.
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm. The examples include logistic regression, density estimation and classification with hinge loss. Least squares regression is also discussed.