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作者：Albert, Melisande; Bouret, Yann; Fromont, Magalie; Reynaud-Bouret, Patricia
作者单位：Universite Cote d'Azur; Universite Cote d'Azur; Universite Rennes 2; Universite de Rennes
摘要：Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are resealed general U-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap ...
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作者：Fan, Jianqing; Rigollet, Philippe; Wang, Weichen
作者单位：Princeton University; Massachusetts Institute of Technology (MIT)
摘要：High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other l(r) norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are spar...
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作者：Gao, Chao; Zhou, Harrison H.
作者单位：Yale University
摘要：Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA were established under various interesting settings. On the other side, Bayesian methods are becoming...
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作者：Einmahl, John H. J.; Li, Jun; Lui, Regina Y.
作者单位：Tilburg University; University of California System; University of California Riverside; Rutgers University System; Rutgers University New Brunswick
摘要：Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical half-space depth usel...
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作者：Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong
作者单位：Stanford University; Harvard University; Harvard University
摘要：In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a functio...
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作者：Tuo, Rui; Wu, C. F. Jeff
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University System of Georgia; Georgia Institute of Technology
摘要：Many computer models contain unknown parameters which need to be estimated using physical observations. Tuo and Wu (2014) show that the calibration method based on Gaussian process models proposed by Kennedy and O'Hagan [J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 (2001) 425-464] may lead to an unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L-2 calibration, and...
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作者：Szabo, Botond; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; University of Amsterdam
摘要：We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of prescribed posterior probability in the posterior distribution of the chosen regularity. We show that such an adaptive Bayes credible set gives correct uncertainty quantification of polished tail parameters, in the sense of high probability of coverage of such p...
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作者：Chen, Jia; Li, Degui; Liang, Hua; Wang, Suojin
作者单位：University of York - UK; University of York - UK; George Washington University; Texas A&M University System; Texas A&M University College Station
摘要：In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations (GEE) is introduced to estimate the two parameter vectors as well as the unknown link function. Under some mild conditions, we derive the asymptotic properties of the proposed parametric and nonp...
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作者：Bruna, Joan; Mallat, Stephane; Bacry, Emmanuel; Muzy, Jean-Francois
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions,...
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作者：Chen, Hao; Zhang, Nancy
作者单位：University of California System; University of California Davis; University of Pennsylvania
摘要：We consider the testing and estimation of change-points-locations where the distribution abruptly changes-in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations, is proposed. The graph-based approach is nonparametric, and can be applied to any data set as long as an informative similarity measure on the sample space can be defined. Accurate analytic approximations to the significance of graph-based scan statistics for both...
