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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order of magnitude as n, the number of observations used to estimate the parameters. The Markowitz problem in Finance is a subcase of our study. Assuming normality and independence of the observations we relate the efficient frontier computed empirically to the t...
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作者：Hallin, Marc; Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles; Universite de Lille
摘要：This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Davis (1977) and Tyler (1981, 1983). The rank-based tests address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general scatter matrices. T...
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作者：Golubev, Yuri
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper deals with recovering an unknown vector theta from the noisy data Y = A theta + sigma xi, where A is a known (m x n)-matrix and xi is a white Gaussian noise. It is assumed that n is large and A may be severely ill-posed. Therefore, in order to estimate theta, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data Y. For spectral regularization methods related to the so-called ordered smoothers [see Kneip Ann. Statis...
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作者：Yang, Min
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Deriving optimal designs for nonlinear models is, in general, challenging. One crucial step is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza Phenomenon states that under a (p - 1)th-degree polynomial regression model, any optimal design can be based on at most p design points, the minimum number of support points such that all p...
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作者：Jiang, Jiancheng; Fan, Yingying; Fan, Jianqing
作者单位：University of North Carolina; University of North Carolina Charlotte; University of Southern California; Princeton University
摘要：Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulat...
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作者：Kong, Linglong; Mizera, Ivan
作者单位：University of Alberta
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作者：Li, Bing; Kim, Min Kyung; Altman, Naomi
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables-for example, the voltage measured at different channels and times in electroencephalography data. For these applications, it is desirable to preserve the array structure of the reduced predictor (e.g., time versus channel), but this cannot be achieved within the...
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作者：Cai, T. Tony; Jin, Jiashun
作者单位：University of Pennsylvania; Carnegie Mellon University
摘要：An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several important problems, including the evaluation of the minimax rate of convergence and the construction of rate-optimal estimators, remain open. In this paper, we consider optimal estimation of the null density and the proportion of nonnull effects. Both minima...
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作者：Leonenko, Nikolai; Pronzato, Luc
作者单位：Cardiff University; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
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作者：Fan, Jianqing; Feng, Yang; Niu, Yue S.
作者单位：Princeton University; Columbia University; University of Arizona
摘要：Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman-Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the samp...
