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作者：Royset, Johannes O.; Wets, Roger J-B
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School; University of California System; University of California Davis
摘要：We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the framework addresses situations where the class of functions is complex involving information and assumptions about shape, pointwise bounds, location of modes, height at modes, location of level-sets, values of moments, size of subgradients, continuity, distance t...
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作者：Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite de Toulouse; Universite Toulouse 1 Capitole
摘要：Motivated by the fact that circular or spherical data are often much concentrated around a location theta, we consider inference about theta under high concentration asymptotic scenarios for which the probability of any fixed spherical cap centered at theta converges to one as the sample size n diverges to infinity. Rather than restricting to Fisher-von Mises-Langevin distributions, we consider a much broader, semiparametric, class of rotationally symmetric distributions indexed by the locatio...
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作者：Huang, Hanwen
作者单位：University System of Georgia; University of Georgia
摘要：Mean square error (MSE) of the estimator can be used to evaluate the performance of a regression model. In this paper, we derive the asymptotic MSE of l(1)-penalized robust estimators in the limit of both sample size n and dimension p going to infinity with fixed ratio n/p -> delta. We focus on the l(1)-penalized least absolute deviation and l(1)-penalized Huber's regressions. Our analytic study shows the appearance of a sharp phase transition in the two-dimensional sparsity-undersampling phas...
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作者：Castillo, Ismael; Roquain, Etienne
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.
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作者：Kuchibhotla, Arun K.; Brown, Lawrence D.; Buja, Andreas; Cai, Junhui; George, Edward, I; Zhao, Linda H.
作者单位：University of Pennsylvania
摘要：Modern data-driven approaches to modeling make extensive use of co-variate/model selection. Such selection incurs a cost: it invalidates classical statistical inference. A conservative remedy to the problem was proposed by Berk et al. (Ann. Statist. 41 (2013) 802-837) and further extended by Bachoc, Preinerstorfer and Steinberger (2016). These proposals, labeled PoSI methods, provide valid inference after arbitrary model selection. They are computationally NP-hard and have limitations in their...
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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：Aue, Alexander; van Delft, Anne
作者单位：University of California System; University of California Davis; Ruhr University Bochum
摘要：Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, expli...
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作者：Wang, Shuaiwen; Weng, Haolei; Maleki, Arian
作者单位：Columbia University; Michigan State University
摘要：We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations n grows at the same rate as the number of predictors p. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds this estimate to select the important predictors. The asymptotic false discovery proportion (AFDP) and...
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作者：Ledoit, Olivier; Wolf, Michael
作者单位：University of Zurich
摘要：This paper establishes the first analytical formula for nonlinear shrinkage estimation of large-dimensional covariancematrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were of numerical nature: QuEST requires numerical inversion of a complex equation from random matrix theory whereas NERCOME is based on a s...
