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作者：Li, Jun; Liu, Regina Y.
作者单位：University of California System; University of California Riverside; Rutgers University System; Rutgers University New Brunswick
摘要：This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistics. These multivariate spacings can be viewed as a data-driven realization of the so-called statistica...
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作者：Zou, Hui; Yuan, Ming
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University System of Georgia; Georgia Institute of Technology
摘要：Coefficient estimation and variable selection in multiple linear regression is routinely done in the (penalized) least squares (LS) framework. The concept of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348-1360] characterizes the optimal behavior of a model selection procedure. However, the least-squares oracle theory breaks down if the error variance is infinite. In the current paper we propose a new regression method called composite quantile regressi...
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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 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. Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 10311063] proved that both types of estimators converge globally and locally at rate n(1/3). We use these results to derive the local limiting distributions of the estimators. The limiting distribution of the naive esti...
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作者：Anderes, Ethan B.; Stein, Michael L.
作者单位：University of California System; University of California Berkeley; University of Chicago
摘要：This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on R-2 based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package-from model assumptions to algorithmic recovery of the deformation-for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.
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作者：Leonenko, Nikolai; Pronzat, Luc; Savani, Vippal
作者单位：Cardiff University; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：A class of estimators of the Renyi and Tsallis entropies of an unknown distribution f in R-m is presented. These estimators are based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f. We show that entropies of any order q, including Shannon's entropy, can be estimated consistently with minimal assumptions on f. Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two d...
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作者：Zhou, Jianhui; He, Xuming
作者单位：University of Virginia; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The curse of dimensionality has remained a challenge for high-dimensional data analysis in statistics'. The sliced inverse regression (SIR) and canonical correlation (CANCOR) methods aim to reduce the dimensionality of data by replacing the explanatory variables with a small number of composite directions without losing much information. However, the estimated composite directions generally involve all of the variables, making their interpretation difficult. To simplify the direction estimates...
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：The theory of adaptive estimation and oracle inequalities for the case of Gaussian-shift-finite-interval experiments has made significant progress in recent years. In particular, sharp-minimax adaptive estimators and exact exponential-type oracle inequalities have been suggested for a vast set of functions including analytic and Sobolev with any positive index as well as for Efromovich-Pinsker and Stein blockwise-shrinkage estimators. Is it possible to obtain similar results for a more interes...
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作者：Jupp, P. E.
作者单位：University of St Andrews
摘要：Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are proposed. These tests are invariant under isometries; and are consistent against all alternatives. The large-sample asymptotic null distributions are given.
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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 regularizing a covariance matrix of p variables estimated from it observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n -> 0, and obtain explicit rates. The results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity. We discuss an intuitive resamp...
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作者：Buehlmann, Peter; Meier, Lukas
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
