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作者：Tang, Yin; Li, Bing
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null distribution, or require ...
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作者：Zhang, Yunyi; Paparoditis, Efstathios; Politis, Dimitris n.
作者单位：The Chinese University of Hong Kong, Shenzhen; University of California System; University of California San Diego; University of California System; University of California San Diego
摘要：Strict stationarity is an assumption commonly used in time-series analysis in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimators obtained by fitting a (l...
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作者：Yan, Yuling; Wang, Kaizheng; Rigollet, Philippe
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University; Columbia University; Massachusetts Institute of Technology (MIT)
摘要：Gaussian mixture models form a flexible and expressive parametric family of distributions that has found a variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a computational perspective. Currently, only moment-based methods enjoy theoretical guarantees while likelihood-based methods are dominated by heuristics such as Expectation-Maximization that are known to fail in simple examples. In this work, we propose a new algorithm to compute the n...
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作者：Chetelat, Didier
作者单位：Universite de Montreal; Polytechnique Montreal
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作者：Katsevich, Anya; Rigollet, Philippe
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals, and a viable alternative to the more established paradigm of Markov chain Monte Carlo. However, little is known about the approximation accuracy of VI. In this work, we bound the TV error and the mean and covariance approximation error of Gaussian VI in terms...
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作者：Li, Jiaqi; Chen, Likai; Wang, Weining; Wu, Wei biao
作者单位：Washington University (WUSTL); University of Groningen; University of Chicago
摘要：We propose an inference method for detecting multiple change points inhigh-dimensional time series, targeting dense or spatially clustered signals.Our method aggregates moving sum (MOSUM) statistics cross-sectionallyby an2-norm and maximizes them over time. We further introduce anovel Two-Way MOSUM, which utilizes spatial-temporal moving regionsto search for breaks, with the added advantage of enhancing testing powerwhen breaks occur in only a few groups. The limiting distribution of an2-aggre...
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作者：Marandon, Ariane; Lei, Lihua; Mary, David; Roquain, Etienne
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Stanford University; Universite Cote d'Azur; Observatoire de la Cote d'Azur
摘要：This paper studies the semisupervised novelty detection problem where a set of typical measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast to classical FDR-con...
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作者：Drees, Holger
作者单位：University of Hamburg
摘要：We analyze the extreme value dependence of independent, not necesMore specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral measure to devise consistent tests for the null hypothesis that the spectral measure does not ch...
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作者：Han, Qiyang
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：In the standard Gaussian linear measurement model Y = X mu 0 + xi is an element of Rm with a fixed noise level sigma > 0, we consider the problem of estimating the unknown signal mu 0 under a convex constraint mu 0 is an element of K , where K is a closed convex set in Rn. We show that the risk of the natural convex constrained least squares estimator (LSE) mu?(sigma) can be characterized exactly in high dimensional limits, by that of the convex constrained LSE mu ?seQ K in the corresponding G...
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作者：Blanchard, Moise; Jaillet, Patrick
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in this regression context. We consider universal consistency, which asks for strong consistency of a learner without restrictions on the value responses. Our analysis shows that such an objective is achievable for a significantly larger class of instance sequen...
