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作者：Lei, Jing
作者单位：Carnegie Mellon University
摘要：The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models with finer structures...
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作者：Bonhomme, Stephane; Jochmans, Koen; Robin, Jean-Marc
作者单位：University of Chicago; Institut d'Etudes Politiques Paris (Sciences Po); University of London; University College London
摘要：A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this joint-diagonalization problem. Algorit...
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作者：Chen, Yen-Chi; Genovese, Christopher R.; Tibshirani, Ryan J.; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：Modal regression estimates the local modes of the distribution of Y given X = x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of Y and X. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is use...
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作者：Luedtke, Alexander R.; van der Laan, Mark J.
作者单位：University of California System; University of California Berkeley
摘要：We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular and asymptotically linear (RAL) estimator of the optimal value. The s...
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作者：Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly
作者单位：Ruhr University Bochum; Cardiff University
摘要：This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimat...
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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. ...
