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作者：Nadler, Boaz
作者单位：Weizmann Institute of Science
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作者：Zhang, Xiaoke; Wang, Jane-Ling
作者单位：University of Delaware; University of California System; University of California Davis
摘要：Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling plan, be it dense,...
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作者：Han, Xiao; Pan, Guangming; Zhang, Bo
作者单位：Nanyang Technological University
摘要：Let A(p) = YY*/m and B-p = XX*/n be two independent random matrices where X = (X-ij)(pxn) and Y = (Y-ij)(pxm) respectively consist of real (or complex) independent random variables with EXij = EYij = 0, E vertical bar X-ij vertical bar(2) = E vertical bar Y-ij vertical bar(2) = 1. Denote by lambda(1) the largest root of the determinantal equation det(lambda A(p) - B-p) = 0. We establish the Tracy-Widom type universality for lambda(1) under some moment conditions on X-ij and Y-ij when p/m and p...
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作者：Li, Ke
作者单位：International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT)
摘要：We consider the problem of testing multiple quantum hypotheses {rho(circle times n)(1) ,..., rho(circle times n)(r)},where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability P-e decays exponentially to zero, that is, P-e = exp{-xi n + o(n)}. However, this error exponent xi is generally unknown, except for the case that r = 2. In this paper, we solve the long-standing open problem of identi...
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作者：Yuan, Ming; Zhou, Ding-Xuan
作者单位：University of Wisconsin System; University of Wisconsin Madison; City University of Hong Kong
摘要：We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal a behavior universal to this class of high dimensional problems. In the sparse regime when the components are sufficiently smooth or the dimensionality is sufficiently large, the optimal rates are identical to those for high dimensional linear regression and, therefore, there is no additional cost to entertain a nonparametric model. ...
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作者：Cheng, Ming-Yen; Fan, Jianqing
作者单位：National Taiwan University; Princeton University
摘要：Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape constraints, estimatio...
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作者：Li, Runze
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
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作者：Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：Yale University
摘要：Recently, network analysis has gained more and more attention in statistics, as well as in computer science, probability and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives minimax rates of the mis-...
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作者：El Karoui, Noureddine; Wu, Hau-Tieng
作者单位：University of California System; University of California Berkeley; University of Toronto
摘要：Recently, several data analytic techniques based on graph connection Laplacian (GCL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is observed without noise. We study the impact of additive noise on these methods and show that they are remarkably robust. As a by-product of our analysis, we propose modifications of the standard algorithms that increase their robustness to noise. We illustrate our...
