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作者：Chen, Song Xi; Zhong, Ping-Shou
作者单位：Iowa State University; Peking University
摘要：We carry out ANOVA comparisons of multiple treatments for longitudinal studies with missing values. The treatment effects are modeled semiparametrically via a partially linear regression which is flexible in quantifying the time effects of treatments. The empirical likelihood is employed to formulate model-robust nonparametric ANOVA tests for treatment effects with respect to covariates, the nonparametric time-effect functions and interactions between covariates and time. The proposed tests ca...
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作者：Chen, Xin; Zou, Changliang; Cook, R. Dennis
作者单位：Syracuse University; Nankai University; Nankai University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is large. The standard SDR methods suffer because the estimated linear combinations usually consist of all original predictors, making it difficult to interpret. In this paper, we propose a unified method-coordinate-independent sparse estimation (CISE)-that can ...
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作者：Li, Yehua; Hsing, Tailen
作者单位：University System of Georgia; University of Georgia; University of Michigan System; University of Michigan
摘要：In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these projections is called the effective dimension reduction (EDR) space. To determine the dimensionality of the EDR space, we focus on the leading principal component scores of the predictor, and propose two sequential chi(2) testing procedures under the assumption that...
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作者：Seregin, Arseni; Wellner, Jon A.
作者单位：University of Washington; University of Washington Seattle
摘要：We study estimation of multivariate densities p of the form p(x) = h(g(x)) for x is an element of R-d and for a fixed monotone function h and an unknown convex function g. The canonical example is h(y) = e(-y) for y is an element of R; in this case, the resulting class of densities P(e(-y)) = {p = exp(-g) : g is convex} is well known as the class of log-concave densities. Other functions h allow for classes of densities with heavier tails than the log-concave class. We first investigate when t...
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作者：Arlot, Sylvain; Blanchard, Gilles; Roquain, Etienne
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Inria; Universite PSL; Ecole Normale Superieure (ENS); Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：We Study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first ...
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作者：de Jonge, R.; van Zanten, J. H.
作者单位：Eindhoven University of Technology
摘要：We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a Gaussian kernel, an inverse gamma bandwidth, and Gaussian mixing weights.
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作者：Koltchinskii, Vladimir; Yuan, Ming
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L-2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the problem is sparse. T...
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作者：Botev, Z. I.; Grotowski, J. F.; Kroese, D. P.
作者单位：University of Queensland
摘要：We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.
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作者：Lee, Young Kyung; Mammen, Enno; Park, Byeong U.
作者单位：Kangwon National University; University of Mannheim; Seoul National University (SNU)
摘要：In this paper, we study the ordinary backfitting and smooth backfitting as methods of fitting additive quantile models. We show that these backfitting quantile estimators are asymptotically equivalent to the corresponding backfitting estimators of the additive components in a specially-designed additive mean regression model. This implies that the theoretical properties of the backfitting quantile estimators are not unlike those of backfitting mean regression estimators. We also assess the fin...
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作者：Park, Byeong U.; Jeong, Seok-Oh; Simar, Leopold
作者单位：Seoul National University (SNU); Hankuk University Foreign Studies; Hankuk University Foreign Studies
摘要：Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs x outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs x outputs space. So far, only the statistical properties of the smallest convex pol...
