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作者：Cai, T. Tony; Zhang, Cun-Hui; Zhou, Harrison H.
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick; Yale University
摘要：Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet been developed. In this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and Frobenius norm. It is shown that optimal procedures under the two norms are different and consequently matrix es...
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作者：Yu, Yaming
作者单位：University of California System; University of California Irvine
摘要：Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379-1389] or computing optimal designs. A conjecture of Titterington [Appl. Stat. 27(1978) 227-234] is confirmed as a consequence. Optimal designs for logistic regression are used as an illustration.
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作者：Kyung, Minjung; Gill, Jeff; Casella, George
作者单位：State University System of Florida; University of Florida; Washington University (WUSTL)
摘要：We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process...
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作者：Arlot, Sylvain; Blanchard, Gilles; Roquain, Etienne
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Inria; 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：In the context of correlated Multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one- and two-sided multiple testing problem for the mean values of its coordinates. We address this problem by using the confidence regions developed in the companion paper [Ann. Statist. (2009), to appear...
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作者：Fan, Jianqing; Song, Rui
作者单位：Princeton University; Colorado State University System; Colorado State University Fort Collins
摘要：Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with Gaussian covariates and responses. In this pa...
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作者：Wang, Jane-Ling; Xue, Liugen; Zhu, Lixing; Chong, Yun Sam
作者单位：University of California System; University of California Davis; Beijing University of Technology; Hong Kong Baptist University
摘要：In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is ...
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作者：Hall, Peter; Jin, Jiashun
作者单位：University of Melbourne; University of California System; University of California Davis; Carnegie Mellon University
摘要：Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables are correlated. In this paper we show that, by exploiting the nature of the correlation, performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer. Indeed, it turns out that the case of in...
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作者：Samworth, R. J.; Wand, M. P.
作者单位：University of Cambridge; University of Cambridge; University of Wollongong
摘要：We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.
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作者：Belomestny, Denis
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider the problem of estimating the fractional order of a Levy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration a...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We place Ourselves in the setting of high-dimensional statistical inference where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n. We consider the spectrum of certain kernel random matrices, in particular n x n matrices whose (i, j)th entry is f(X-i' X-j/p) or f(vertical bar vertical bar X-i - X-j vertical bar vertical bar(2)/p) where p is the dimension of the data, and X-i are independent data vectors. Here f is assumed to b...
