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作者：Jacod, Jean; Li, Jia; Lia, Zhipeng
作者单位：Universite Paris Cite; Sorbonne Universite; Duke University; University of California System; University of California Los Angeles
摘要：This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting. Specifically, we propo...
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作者：Yuan, Yubai; Qu, Annie
作者单位：University of California System; University of California Irvine
摘要：In network analysis, within-community members are more likely to be connected than between-community members, which is reflected in that the edges within a community are intercorrelated. However, existing probabilistic models for community detection such as the stochastic block model (SBM) are not designed to capture the dependence among edges. In this paper, we propose a new community detection approach to incorporate intracommunity dependence of connectivities through the Bahadur representat...
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作者：Chan, Ngai Hang; Ng, Wai Leong; Yau, Chun Yip; Yu, Haihan
作者单位：Chinese University of Hong Kong; Hang Seng University of Hong Kong; Iowa State University
摘要：This paper establishes asymptotic theory for optimal estimation of change points in general time series models under alpha-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real data applications ...
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作者：Chen, Louis H. Y.
作者单位：National University of Singapore
摘要：This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it provides glimpses into the many approaches to constructing Stein identities and the diverse applications of Stein's method to mathematical problems. It also includes anecdotes of historical interest, including how Stein discovered his method and how I found an ...
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作者：Duanmu, Haosui; Roy, Daniel M.
作者单位：University of Toronto
摘要：For finite parameter spaces, among decision procedures with finite risk functions, a decision procedure is extended admissible if and only if it is Bayes. Various relaxations of this classical equivalence have been established for infinite parameter spaces, but these extensions are each subject to technical conditions that limit their applicability, especially to modern (semi and nonparametric) statistical problems. Using results in mathematical logic and nonstandard analysis, we extend this e...
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作者：Strawderman, William E.
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Charles Stein made fundamental contributions to admissibility and inadmissibility in estimation and testing. This paper surveys some of the more important ones. Particular attention will be paid to his monumentally important, and at the time, incredibly surprising discovery of the inadmissibility of the usual estimator of the mean in three and higher dimensions. His result on admissibility of Pitman's estimator of a mean in one and two dimensions, and his results on estimation of a mean matrix...
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作者：Luedtke, Alex; Bibaut, Aurelien; van der Laan, Mark
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
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作者：Andrieu, Christophe; Livingstone, Samuel
作者单位：University of Bristol; University of London; University College London
摘要：Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key role in their development, while the self-adjointness of associated operators together with the use of classical functional analysis techniques on Hilbert spaces have led to powerful and practically successful tools to characterise and compare their performance. Similar results for algorithms relying on nonreversible Markov processes are scarce. We show that for...
