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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 ...
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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...
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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.
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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...
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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] ...
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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.
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作者：Bickel, Peter J.; Levina, Elizaveta
作者单位：University of California System; University of California Berkeley; University of Michigan System; University of Michigan
摘要：This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (log p)/n -> 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned families of covariance matrices. We also introduce an analogue of the Gaussian white noise model and ...
