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作者：McElroy, Tucker S.; Holan, Scott H.
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovariance matrix. We also provide a comprehensive treatment of the asymptotic theory for two-dimensional rand...
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作者：Fryzlewicz, Piotr
作者单位：University of London; London School Economics & Political Science
摘要：We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of localisation, WBS does not re...
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作者：Liu, Weidong; Shao, Qi-Man
作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; Chinese University of Hong Kong
摘要：Applying the Benjamini and Hochberg (B H) method to multiple Student's t tests is a popular technique for gene selection in microarray data analysis. Given the nonnormality of the population, the true p-values of the hypothesis tests are typically unknown. Hence it is common to use the standard normal distribution N(0, 1), Student's t distribution t(n-1) or the bootstrap method to estimate the p-values. In this paper, we prove that when the population has the finite 4th moment and the dimensio...
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作者：Fan, Jianqing; Ke, Zheng Tracy
作者单位：Princeton University
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作者：Onatski, Alexei; Moreira, Marcelo J.; Hallin, Marc
作者单位：University of Cambridge; Getulio Vargas Foundation; Universite Libre de Bruxelles; Princeton University
摘要：This paper applies Le Cam's asymptotic theory of statistical experiments to the signal detection problem in high dimension. We consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the Gaussian asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. Those asymptotic p...
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作者：Buehlmann, Peter; Peters, Jonas; Ernest, Jan
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structur...
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作者：Ke, Zheng Tracy; Jin, Jiashun; Fan, Jianqing
作者单位：University of Chicago; Carnegie Mellon University; Princeton University
摘要：Consider a linear model Y = X beta +z, where X = X-n,X-p and z similar to N(0, In). The vector beta is unknown but is sparse in the sense that most of its coordinates are 0. The main interest is to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya [In Change-Point Problems (South Had...
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作者：Castillo, Ismael; Nickl, Richard
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Cambridge
摘要：We continue the investigation of Bernstein- von Mises theorems for non-parametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined, and prove Bernstein- von Mises theorems for a variety of priors in the setting of Gaussian nonparametric regression and in the i.i.d. sampling model. From these results we deduce several applications where posterior-based inference coincides with efficient f...
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作者：Chernozhukov, Victor; Chetverikov, Dents; Kato, Kengo
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
摘要：Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Gine and Nickl [Probab. Theory Related Fields 143 (2009) 569-596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance function as that of the ...
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作者：Chakraborty, Anirvan; Chaudhuri, Probal
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The spatial distribution has been widely used to develop various non-parametric procedures for finite dimensional multivariate data. In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach spaces. Many technical difficulties are encountered in such spaces that are primarily due to the noncompactness of the closed unit ball. In this work, we prove some Glivenko-Cantelli and Donsker-type results for the empirical spatial distribution process in i...
