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作者：Ho, Nhat; Nguyen, Xuanlong
作者单位：University of Michigan System; University of Michigan
摘要：We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures and some variants of finite mixture models, including the setting where the number of mixing components is bounded but unknown. These models belong to what we call weakly identifiable classes, which exhibit specific interactions among mixing parameters driven by the algebraic structures of the class of kernel densities ...
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作者：Gadat, Sebastien; Klein, Thierry; Marteau, Clement
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Given an n-sample of random vectors (X-i, Y-i)(1 <= i <= n) whose joint law is unknown, the long-standing problem of supervised classification aims to optimally predict the label Y of a given new observation X. In this context, the k-nearest neighbor rule is a popular flexible and intuitive method in non parametric situations. Even if this algorithm is commonly used in the machine learning and statistics communities, less is known about its prediction ability in general finite dimensional spac...
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作者：Yan, Ting; Leng, Chenlei; Zhu, Ji
作者单位：Central China Normal University; University of Warwick; University of Michigan System; University of Michigan
摘要：Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and the asymptotic norma...
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作者：Chang, Jinyuan; Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Southwestern University of Finance & Economics - China; University of Melbourne; Chinese University of Hong Kong; Princeton University
摘要：Two-sample U-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramer-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t...
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作者：Pillai, Natesh S.; Meng, Xiao-Li
作者单位：Harvard University
摘要：The Cauchy distribution is usually presented as a mathematical curiosity, an exception to the Law of Large Numbers, or even as an Evil distribution in some introductory courses. It therefore surprised us when Drton and Xiao [Bernoulli 22 (2016) 38-59] proved the following result for m = 2 and conjectured it for m >= 3. Let X = (X-1,...,X-m) and Y = (Y-1 ,...,Y-m) be i.i.d. N(0, Sigma), where Sigma = {sigma(ij)} >= 0 is an m x m and arbitrary covariance matrix with sigma(jj) > 0 for all 1 <= j ...
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作者：Petersen, Alexander; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used Hilbert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hilbert space of functions through a continuous and inver...
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作者：Arias-Castro, Ery; Verzelen, Nicolas
作者单位：University of California System; University of California San Diego; INRAE
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作者：Gu, Yuwen; Zou, Hui
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Asymmetric least squares regression is an important method that has wide applications in statistics, econometrics and finance. The existing work on asymmetric least squares only considers the traditional low dimension and large sample setting. In this paper, we systematically study the Sparse Asymmetric LEast Squares (SALES) regression under high dimensions where the penalty functions include the Lasso and nonconvex penalties. We develop a unified efficient algorithm for fitting SALES and esta...
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作者：Shpitser, Ilya; Tchetgen, Eric Tchetgen
作者单位：Johns Hopkins University; Harvard University; Harvard T.H. Chan School of Public Health
摘要：Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal mo...
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作者：Zhao, Tianqi; Cheng, Guang; Liu, Han
作者单位：Princeton University; Purdue University System; Purdue University
摘要：We consider a partially linear framework for modeling massive heterogeneous data. The major goal is to extract common features across all subpopulations while exploring heterogeneity of each subpopulation. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (nonasymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. This oracle result holds when the number of subpopulations does not grow too fast. A p...
