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作者：Sanders, Jaron; Proutiere, Alexandre; Yun, Se-Young
作者单位：Royal Institute of Technology; Delft University of Technology; Korea Advanced Institute of Science & Technology (KAIST)
摘要：This paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the n possible states are divided into a finite number of K groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One observes a trajectory of the Markov chain, and the objective is to recover, from this observation only, the (initially unknown) clusters. In this paper, ...
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作者：Dubey, Paromita; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of the data sequence changes abruptly in terms of either its Frechet mean, Frechet variance or both. The proposed method is based on comparisons of Frechet variances before and after putative change-point locations and does not require a tuning parameter, excep...
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作者：Han, Yuefeng; Wu, Wei Biao
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Chicago
摘要：The paper introduces a new test for testing structures of covariances for high dimensional vectors and the data dimension can be much larger than the sample size. Under proper normalization, central and noncentral limit theorems are established. The asymptotic theory is attained without imposing any explicit restriction between data dimension and sample size. To facilitate the related statistical inference, we propose the balanced Rademacher weighted differencing scheme, which is also the dele...
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作者：Li, Zeng; Han, Fang; Yao, Jianfeng
作者单位：Southern University of Science & Technology; University of Washington; University of Washington Seattle; University of Hong Kong
摘要：This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow proportionally. The form of the joint limiting distribution is applied to conduct Johnson-Graybill-type tests, a family of approaches testing for signals in a statistical model. For this, higher order correction is further made, helping alleviate the impact of finit...
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作者：Katsevich, Eugene; Ramdas, Aaditya
作者单位：Carnegie Mellon University
摘要：While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (Statist. Sci. 26 (2011) 584-597) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds on the false discovery proportion (FDP) of the chosen set. In this paper, we propose a new class of such simultaneous FDP bounds, tailored for nested sequences of rejection sets. While most existing simultaneous FDP bounds are bas...
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作者：Comte, Fabienne; Genon-Catalot, Valentine
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider N independent stochastic processes (X-i(t), t is an element of [0, T]), i = 1, ..., N, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval [0, T] where T is fixed. We study nonparametric estimation of the drift function on a given subset A of R. Projection estimators are defined on finite dimensional subsets of L-2 (A, dx). We stress that the set A may be compact or not and the diffusion coefficient may be bounde...
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作者：Deng, Hang; Zhang, Cun-Hui
摘要：The Bonferroni adjustment, or the union bound, is commonly used to study rate optimality properties of statistical methods in high-dimensional problems. However, in practice, the Bonferroni adjustment is overly conservative. The extreme value theory has been proven to provide more accurate multiplicity adjustments in a number of settings, but only on an ad hoc basis. Recently, Gaussian approximation has been used to justify bootstrap adjustments in large scale simultaneous inference in some ge...
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作者：Edelmann, Dominic; Richards, Donald; Vogel, Daniel
作者单位：Helmholtz Association; German Cancer Research Center (DKFZ); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Aberdeen
摘要：The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite second moments. Applications are provided to hypothesis testing on a data set from materials science and to multivariate statistical quality control. The distance standard deviation is compared to classical scale measures for inference on the spre...
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作者：Kim, Ilmun; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：In this work, we generalize the Cramer-von Mises statistic via projection averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavytailed data and minimax rate optimal against a certain class of alternatives. Our test statistic is completely free of tuning parameters and is computationally efficient even in high dimensions. When the dimension tends to infinity, the proposed test is shown to have co...
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作者：Durmus, Alain; Moulines, Eric; Saksman, Eero
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); HSE University (National Research University Higher School of Economics); University of Helsinki
摘要：Hamiltonian Monte Carlo (HMC) is currently one of the most popular Markov Chain Monte Carlo algorithms to sample smooth distributions over continuous state space. This paper discusses the irreducibility and geometric ergodicity of the HMC algorithm. We consider cases where the number of steps of the Stormer-Verlet integrator is either fixed or random. Under mild conditions on the potential U associated with target distribution pi, we first show that the Markov kernel associated to the HMC algo...
