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作者：Cai, T. Tony; Han, Xiao; Pan, Guangming
作者单位：University of Pennsylvania; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Nanyang Technological University; Nanyang Technological University
摘要：We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance model with divergent spiked eigenvalues, while the other eigenvalues are bounded but otherwise arbitrary. The limiting normal distribution for the spiked sample eigenvalues is established. It has distinct features that the asymptotic mean relies on not only the population spikes but also the nonspikes and that the asymptotic variance in...
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作者：Kim, Kyongwon; Li, Bing; Yu, Zhou; Li, Lexin
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; East China Normal University; University of California System; University of California Berkeley
摘要：The methodologies of sufficient dimension reduction have undergone extensive developments in the past three decades. However, there has been a lack of systematic and rigorous development of post dimension reduction inference, which has seriously hindered its applications. The current common practice is to treat the estimated sufficient predictors as the true predictors and use them as the starting point of the downstream statistical inference. However, this naive inference approach would gross...
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作者：Dette, Holger; Kokot, Kevin; Aue, Alexander
作者单位：Ruhr University Bochum; University of California System; University of California Davis
摘要：Functional data analysis is typically conducted within the L-2-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems, often based on dimension reduction techniques such as functional principal component analysis. At the same time, there have recently been a number of publications that sidestep dimension reduction steps and focus on a fully functional L-2-methodology. This pa...
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作者：Koskela, Jere; Jenkins, Paul A.; Johansen, Adam M.; Spano, Dario
作者单位：University of Warwick; University of Warwick
摘要：We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit i...
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作者：Deng, Hang; Zhang, Cun-Hui
摘要：The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on an ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous inference in some ge...
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作者：Edelmann, Dominic; Richards, Donald; Vogel, Daniel
作者单位：Helmholtz Association; German Cancer Research Center (DKFZ); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Aberdeen
摘要：The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite second moments. Applications are provided to hypothesis testing on a data set from materials science and to multivariate statistical quality control. The distance standard deviation is compared to classical scale measures for inference on the spre...
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作者：Kim, Ilmun; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：In this work, we generalize the Cramer-von Mises statistic via projection averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavytailed data and minimax rate optimal against a certain class of alternatives. Our test statistic is completely free of tuning parameters and is computationally efficient even in high dimensions. When the dimension tends to infinity, the proposed test is shown to have co...
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作者：Wang, Runmin; Shao, Xiaofeng
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Self-normalization has attracted considerable attention in the recent literature of time series analysis, but its scope of applicability has been limited to low-/fixed-dimensional parameters for low-dimensional time series. In this article, we propose a new formulation of self-normalization for inference about the mean of high-dimensional stationary processes. Our original test statistic is a U-statistic with a trimming parameter to remove the bias caused by weak dependence. Under the framewor...
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作者：Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been investigated for any...
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作者：Jagadeesan, Ravi; Pillai, Natesh S.; Volfovsky, Alexander
作者单位：Harvard University; Harvard University; Duke University
摘要：In this paper, we introduce new, easily implementable designs for drawing causal inference from randomized experiments on networks with interference. Inspired by the idea of matching in observational studies, we introduce the notion of considering a treatment assignment as a quasi-coloring on a graph. Our idea of a perfect quasi-coloring strives to match every treated unit on a given network with a distinct control unit that has identical number of treated and control neighbors. For a wide ran...
