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作者：Hofmann, Thomas; Schoelkopf, Bernhard; Smola, Alexander J.
作者单位：Technical University of Darmstadt; Max Planck Society; NICTA
摘要：We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on...
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作者：Rohde, Angelika
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Within the nonparametric regression model with unknown regression function l and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis l = 0 against a nonparametric alternative is proposed. This test is distribution-free and exact for finite samples even in the heteroscedastic case. It adapts in a certain sense to the unknown smoothness of the regression function under the alternative, and it is uniformly co...
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作者：Coeurjolly, Jean-Francois
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：This paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self-similar Gaussian processes. These estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval [0, 1]. We derive the almost sure convergence and the asymptotic normality for these estimators. The key-ingredient is a Bahadur representation for sample quantiles of nonlinear functions of Gaussian ...
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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：Hallin, Marc; Paindaveine, Davy
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We propose a class of locally and asymptotically optimal tests, based on multivariate ranks and signs for the homogeneity of scatter matrices in M. elliptical populations. Contrary to the existing parametric procedures, these tests remain valid without any moment assumptions, and thus are perfectly robust against heavy-tailed distributions (validity robustness). Nevertheless, they reach semiparametric efficiency bounds at correctly specified elliptical densities and maintain high powers under ...
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作者：Chatterjee, Snigdhansu; Lahiri, Partha; Li, Huilin
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University System of Maryland; University of Maryland College Park
摘要：Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability....
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作者：Lii, Keh-Shin; Rosenblatt, Murray
作者单位：University of California System; University of California Riverside; University of California System; University of California San Diego
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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...
