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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...
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作者：Zheng, Shurong; Bai, Zhidong; Yao, Jianfeng
作者单位：Northeast Normal University - China; Northeast Normal University - China; University of Hong Kong
摘要：Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like moment conditions. In ...
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作者：Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd
作者单位：Aalto University; University of California System; University of California Berkeley
摘要：Mixtures of r independent distributions for two discrete random variables can be represented by matrices of nonnegative rank r. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the set of fixed points of the Expectation-Maximization algorithm, and we study the boundary of the space of matrices with nonnegative rank at most 3. Both of these sets correspond to algebraic varietie...
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作者：Loh, Wei-Liem
作者单位：National University of Singapore
摘要：This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field observations taken along a...
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作者：Ma, Zongming; Wu, Yihong
作者单位：University of Pennsylvania; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a complexity-theoretic perspective, we consider a sequence of discretized models which are asymptotically equivalent to the Gaussian model. Under the hypothesis that the planted clique detection problem cannot be solved in randomized polynomial time when the clique size i...
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作者：Zhang, Ting; Wu, Wei Biao
作者单位：Boston University; University of Chicago
摘要：This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results a...
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作者：Amonenk, Inga S.; Robinson, John
作者单位：University of Sydney
摘要：We introduce a nonparametric test statistic for the permutation test in complete block designs. We find the region in which the statistic exists and consider particularly its properties on the boundary of the region. Further, we prove that saddlepoint approximations for tail probabilities can be obtained inside the interior of this region. Finally, numerical examples are given showing that both accuracy and power of the new statistic improves on these properties of the classical F-statistic un...
