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作者：Han, Qiyang; Wellner, Jon A.
作者单位：University of Washington; University of Washington Seattle
摘要：We study the performance of the least squares estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a pth moment (p >= 1). In such a heavy-tailed regression setting, we show that if the model satisfies a standard entropy condition with exponent alpha is an element of (0, 2), then the L-2 loss of the LSE converges at a rate O-P(n(-1/2+alpha) boolean OR n(-1/2+1/2p)). Such a rate cannot be improved under the entropy condi...
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作者：Han, Xu
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality p and the sample size n can satisfy the NP dimensionality log p = O(n(a)) for some a > 0 [J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 (2008) 849-911]. The current paper aims to simultaneously tackle the universality and effectiveness of sure screening procedures. For the universality, we develop a general and unified framework for nonparametr...
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作者：Chen, Yen-Chi
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper we study the alpha-cluster tree (alpha-tree) under both singular and nonsingular measures. The alpha-tree uses probability contents within a set created by the ordering of points to construct a cluster tree so that it is well defined even for singular measures. We first derive the convergence rate for a density level set around critical points, which leads to the convergence rate for estimating an alpha-tree under nonsingular measures. For singular measures, we study how the kern...
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作者：Alquier, Pierre; Cottet, Vincent; Lecue, Guillaume
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSAE Paris
摘要：We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form (f ) over cap is an element of argmin(f is an element of F) (1/N Sigma(N )(i=1)l(f) (X-i, Y-i) + lambda parallel to f parallel to) when parallel to . parallel to is any norm, F is a convex class of functions and l is a Lipschitz loss function satisfying a Bernstein condition over F. We explore both the bounded and sub-Gaussian stochastic frameworks for the distribution of the f (X-i)'s, wit...
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作者：Tan, Falong; Zhu, Lixing
作者单位：Hunan University; Beijing Normal University; Hong Kong Baptist University
摘要：In this paper, we construct an adaptive-to-model residual-marked empirical process as the base of constructing a goodness-of-fit test for parametric single-index models with diverging number of predictors. To study the relevant asymptotic properties, we first investigate, under the null and alternative hypothesis, the estimation consistency and asymptotically linear representation of the nonlinear least squares estimator for the parameters of interest and then the convergence of the empirical ...
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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：In this paper, the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressi...
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作者：Das, Debraj; Gregory, Karl; Lahiri, S. N.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of South Carolina System; University of South Carolina Columbia; North Carolina State University
摘要：The Adaptive Lasso (Alasso) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] as a modification of the Lasso for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] established that the Alasso estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain fixed-dimensional sett...
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作者：Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Holder density with exponent 0 < s <= 1, with possibly unbounded support, in the low-smoothness reg...
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作者：Tong, Xingwei; Gao, Fuqing; Chen, Kani; Cai, Dingjiao; Sun, Jianguo
作者单位：Beijing Normal University; Wuhan University; Hong Kong University of Science & Technology; Henan University of Economics & Law; University of Missouri System; University of Missouri Columbia
摘要：This paper discusses the transformed linear regression with non-normal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution, respectively. Desp...
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作者：Qin, Qian; Hobert, James P.
作者单位：State University System of Florida; University of Florida
摘要：The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales with sample size, n, and/or number of covariates, p. This article provides a thorough convergence complexity analysis of Albert and Chib's [J. Amer. Statist. Assoc. 88 (1993) 669-679] data augmentation algorithm for the Bayesian probit regression model. The...
