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作者：Vandermeulen, Robert A.; Scott, Clayton D.
作者单位：University of Kaiserslautern; University of Michigan System; University of Michigan
摘要：When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that observations from the mixture model are grouped, such that observations in the same group are known to be drawn from the same mixture component. We precisely characterize the number of observations n per group needed for the mixture model to be identifiable, as a f...
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作者：Das, Debraj; Gregory, Karl; Lahiri, S. N.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of South Carolina System; University of South Carolina Columbia; North Carolina State University
摘要：The Adaptive Lasso (Alasso) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] as a modification of the Lasso for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] established that the Alasso estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain fixed-dimensional sett...
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作者：Lugosi, Gabor; Mendelson, Shahar
作者单位：ICREA; Pompeu Fabra University; Barcelona School of Economics; Technion Israel Institute of Technology; Australian National University
摘要：We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.
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作者：Camerlenghi, Federico; Lijoi, Antonio; Orbanz, Peter; Prunster, Igor
作者单位：University of Milano-Bicocca; Bocconi University; Bocconi University; Columbia University
摘要：Hierarchies of discrete probability measures are remarkably popular as nonparametric priors in applications, arguably due to two key properties: (i) they naturally represent multiple heterogeneous populations; (ii) they produce ties across populations, resulting in a shrinkage property often described as sharing of information. In this paper, we establish a distribution theory for hierarchical random measures that are generated via normalization, thus encompassing both the hierarchical Dirichl...
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作者：Dasgupta, Sayan; Goldberg, Yair; Kosorok, Michael R.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Haifa
摘要：We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed approach.
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作者：Lepski, O., V; Willer, T.
作者单位：Aix-Marseille Universite
摘要：We study the problem of nonparametric estimation under L-p-loss, p is an element of[1, infinity), in the framework of the convolution structure density model on R-d. This observation scheme is a generalization of two classical statistical models, namely density estimation under direct and indirect observations. The original pointwise selection rule from a family of kernel-type estimators is proposed. For the selected estimator, we prove an L-p-norm oracle inequality and several of its conseque...
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作者：Lin, Zhenhua; Yao, Fang
作者单位：National University of Singapore; Peking University
摘要：In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon intrinsic geometric c...
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作者：Zheng, Shurong; Chen, Zhao; Cui, Hengjian; Li, Runze
作者单位：Northeast Normal University - China; Northeast Normal University - China; Capital Normal University; Fudan University; 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
摘要：This paper is concerned with test of significance on high-dimensional covariance structures, and aims to develop a unified framework for testing commonly used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we st...
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作者：Bodnar, Taras; Dette, Holger; Parolya, Nestor
作者单位：Stockholm University; Ruhr University Bochum; Leibniz University Hannover
摘要：In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we study the weak conv...
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作者：Chetelat, Didier; Wells, Martin T.
作者单位：Universite de Montreal; Polytechnique Montreal; Cornell University
摘要：We study the behavior of a real p-dimensional Wishart random matrix with n degrees of freedom when n, p -> infinity but p/n -> 0. We establish the existence of phase transitions when p grows at the order n((K+1)/(K+3)) for every K is an element of N, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the F-conjugate of an absolutely continuous distribution, which is obtained from the Fourier transform of the s...
