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作者：Cao, Xuan; Khare, Kshitij; Ghosh, Malay
作者单位：State University System of Florida; University of Florida
摘要：Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been developed in recent years...
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作者：Chang, Hsin-Wen; McKeague, Ian W.
作者单位：Academia Sinica - Taiwan; Columbia University
摘要：New nonparametric tests for the ordering of multiple survival functions are developed with the possibility of right censorship taken into account. The motivation comes from noninferiority trials with multiple treatments. The proposed tests are based on nonparametric likelihood ratio statistics, which are known to provide more powerful tests than Wald-type procedures, but in this setting have only been studied for pairs of survival functions or in the absence of censoring. We introduce a novel ...
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作者：Chu, Lynna; Chen, Hao
作者单位：University of California System; University of California Davis
摘要：We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information among observations, which can be applied to various data types as long as an informative similarity measure on the sample space can be defined. The existing approach along this line has low power and/or biased estimates for change-points under some common s...
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作者：Hu, Jiang; Li, Weiming; Liu, Zhi; Zhou, Wang
作者单位：Northeast Normal University - China; Northeast Normal University - China; Shanghai University of Finance & Economics; University of Macau; National University of Singapore
摘要：This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of ...
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作者：Rohe, Karl
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Web crawling, snowball sampling, and respondent-driven sampling (RDS) are three types of network sampling techniques used to contact individuals in hard-to-reach populations. This paper studies these procedures as a Markov process on the social network that is indexed by a tree. Each node in this tree corresponds to an observation and each edge in the tree corresponds to a referral. Indexing with a tree (instead of a chain) allows for the sampled units to refer multiple future units into the s...
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作者：Tewes, Johannes; Politis, Dimitris N.; Nordman, Daniel J.
作者单位：Ruhr University Bochum; University of California System; University of California San Diego; Iowa State University
摘要：The block bootstrap approximates sampling distributions from dependent data by resampling data blocks. A fundamental problem is establishing its consistency for the distribution of a sample mean, as a prototypical statistic. We use a structural relationship with subsampling to characterize the bootstrap in a new and general manner. While subsampling and block bootstrap differ, the block bootstrap distribution of a sample mean equals that of a k-fold self-convolution of a subsampling distributi...
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作者：Cuesta-Albertos, Juan A.; Garcia-Portugues, Eduardo; Febrero-Bande, Manuel; Gonzalez-Manteiga, Wenceslao
作者单位：Universidad de Cantabria; Universidade de Santiago de Compostela
摘要：We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that exhibit root-n convergence rates and circumvent the curse of dimensionality. The weak convergence of the empirical process is obtained conditionally on a random direction, whilst th...
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作者：Descary, Marie-Helene; Panaretos, Victor M.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretabilit...
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作者：Chakraborty, Rudrasis; Vemuri, Baba C.
作者单位：State University System of Florida; University of Florida
摘要：A Stiefel manifold of the compact type is often encountered in many fields of engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spaces and performed statistical analysis of data residing in these spaces. In this paper, we present original work involving definition of Gaussian di...
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作者：Aamari, Eddie; Levrard, Clement
作者单位：University of California System; University of California San Diego; Sorbonne Universite; Universite Paris Cite
摘要：Given a noisy sample from a submanifold M subset of R-D, we derive optimal rates for the estimation of tangent spaces TXM, the second fundamental form IIXM and the submanifold M. After motivating their study, we introduce a quantitative class of C-k-submanifolds in analogy with Holder classes. The proposed estimators are based on local polynomials and allow to deal simultaneously with the three problems at stake. Minimax lower bounds are derived using a conditional version of Assouad's lemma w...
