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作者：Zou, Hui; Li, Runze
作者单位：University of Minnesota System; University of Minnesota Twin Cities; 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
摘要：Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function is computationally challenging, because the objective function is nondifferentiable and nonconcave. In this article, we propose a new unified algorithm based on the local linear approximation (LLA) for maximizing the penalized likelihood for a broad class o...
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作者：Rajaratnam, Bala; Massam, Helene; Carvalho, Carlos M.
作者单位：Stanford University; York University - Canada; University of Chicago
摘要：In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the W-PG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278-1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The W-PG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for flexibility in diffe...
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作者：Cai, T. Tony; Wang, Lie
作者单位：University of Pennsylvania
摘要：We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. The estimator is shown to achieve the optimal adaptive rate of convergence under the pointwise squared ...
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作者：Cuesta-Albertos, Juan A.; Matran, Carlos; Mayo-Iscar, Agustin
作者单位：Universidad de Cantabria; Universidad de Valladolid
摘要：Robust estimators of location and dispersion are Often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data Outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with Such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censo...
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作者：Jiang, Wenxin; Tanner, Martin A.
作者单位：Northwestern University
摘要：In the popular approach of Bayesian variable selection (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with I Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (Such as the classification error) and aims at minimizing a risk function without modeling the data probabilistically. This can ...
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作者：Brown, Lawrence D.; George, Edward I.; Xu, Xinyi
作者单位：University of Pennsylvania; University System of Ohio; Ohio State University
摘要：Let X vertical bar mu similar to N-p (mu, upsilon I-x) and Y vertical bar mu similar to N-p (mu, upsilon I-y) be independent p-dimensional multivariate normal vectors with common unknown mean A. Based on observing X = x, we consider the problem of estimating the true predictive density p(y vertical bar mu) of Y under expected Kullback-Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a comple...
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作者：Hoffmann, Marc; Reiss, Markus
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Ruprecht Karls University Heidelberg
摘要：We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rate-optimality and adaptivity properties over Besov classes.
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作者：Xu, Hongquan; Cheng, Ching-Shui
作者单位：University of California System; University of California Los Angeles; University of California System; University of California Berkeley
摘要：Chen and Cheng [Ann. Statist. 34 (2006) 546-558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for 9N/32 <= n <= 5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with 5N/16 factors which is constructed by repeatedly doubling the 2(5-1) design defined by I = ABCDE. This paper develops a general complementary design theory for doubling. For any design obtained by repeated doubling, g...
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作者：Hall, Peter; Lahiri, Soumendra N.
作者单位：University of Melbourne; Texas A&M University System; Texas A&M University College Station
摘要：When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample since we don not have a sample from the target. These and other considerations motivate the development of estimators of distributions, and of related quantities such as moments and quantiles, in errors-in-variables settings. We show that such estimators have curious and unexpected properties. For example, if the distributions of the variable of in...
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作者：Cheng, Guang; Kosorok, Michael R.
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile sampler obtained in Cheng and Kosorok [Ann. Statist. 36 (2008)] is extended to semiparametric models in which the infinite dimensional nuisance parameter may not have a root-n convergence rate. This is a nontrivial extension because it requires a delicate anal...
