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作者：Gregory, Karl; Mammen, Enno; Wahl, Martin
作者单位：University of South Carolina System; University of South Carolina Columbia; Ruprecht Karls University Heidelberg; Humboldt University of Berlin
摘要：In this paper, we discuss the estimation of a nonparametric component f(1) of a nonparametric additive model Y = f(1)(X-1)+ ... + f(q)(X-q) + epsilon. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f(1) in the oracle model Z = f(1)(X-1) + epsilon, for which the additive components f(2),..., f(q) are known. We construct a two-step presmoo...
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作者：Kpotufe, Samory; Martinet, Guillaume
作者单位：Columbia University; Princeton University
摘要：Transfer Learning addresses common situations in Machine Leaning where little or no labeled data is available for a target prediction problem- corresponding to a distribution Q, but much labeled data is available from some related but different data distribution P. This work is concerned with the fundamental limits of transfer, that is, the limits in target performance in terms of (1) sample sizes from P and Q, and (2) differences in data distributions P, Q. In particular, we aim to address pr...
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作者：Lalancette, Michael; Engelke, Sebastian; Volgushev, Stanislav
作者单位：University of Toronto; University of Geneva
摘要：Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the latter setting is sca...
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作者：Fan, Zhou; Sun, Yi; Wang, Zhichao
作者单位：Yale University; University of Chicago; University of California System; University of California San Diego
摘要：We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present in low-dimensional settings. We derive the first-order limits of the principal eigenvalue locations and eigenvector projections in a high-dimensional asymptotic framework, allowing for general population spectral distributions for the random effects and exte...
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作者：Lin, Zhenhua; Muller, Hans-Georg
作者单位：National University of Singapore; University of California System; University of California Davis
摘要：Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for new methodology in this area, we develop a total variation regularization technique for nonparametric Frechet regression, which refers to a regression setting where a response residing in a metric space is paired with a scalar predictor and the target is a ...
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作者：Catalano, Marta; Lijoi, Antonio; Prunster, Igor
作者单位：University of Warwick; Bocconi University
摘要：The proposal and study of dependent Bayesian nonparametric models has been one of the most active research lines in the last two decades, with random vectors of measures representing a natural and popular tool to define them. Nonetheless, a principled approach to understand and quantify the associated dependence structure is still missing. We devise a general, and not model-specific, framework to achieve this task for random measure based models, which consists in: (a) quantify dependence of a...
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作者：Chan, Ngai Hang; Ng, Wai Leong; Yau, Chun Yip; Yu, Haihan
作者单位：Chinese University of Hong Kong; Hang Seng University of Hong Kong; Iowa State University
摘要：This paper establishes asymptotic theory for optimal estimation of change points in general time series models under alpha-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real data applications ...
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作者：Chen, Louis H. Y.
作者单位：National University of Singapore
摘要：This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it provides glimpses into the many approaches to constructing Stein identities and the diverse applications of Stein's method to mathematical problems. It also includes anecdotes of historical interest, including how Stein discovered his method and how I found an ...
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作者：Duanmu, Haosui; Roy, Daniel M.
作者单位：University of Toronto
摘要：For finite parameter spaces, among decision procedures with finite risk functions, a decision procedure is extended admissible if and only if it is Bayes. Various relaxations of this classical equivalence have been established for infinite parameter spaces, but these extensions are each subject to technical conditions that limit their applicability, especially to modern (semi and nonparametric) statistical problems. Using results in mathematical logic and nonstandard analysis, we extend this e...
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作者：Strawderman, William E.
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Charles Stein made fundamental contributions to admissibility and inadmissibility in estimation and testing. This paper surveys some of the more important ones. Particular attention will be paid to his monumentally important, and at the time, incredibly surprising discovery of the inadmissibility of the usual estimator of the mean in three and higher dimensions. His result on admissibility of Pitman's estimator of a mean in one and two dimensions, and his results on estimation of a mean matrix...
