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《Applied Mathematics:A Journal of Chinese Universities》 2017年03期
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Self-normalization:Taming a wild population in a heavy-tailed world

SHAO Qi-man  ZHOU Wen-xin  
【摘要】:The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student's t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical problems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robustness property of Studentization/self-normalization against heavy-tailed sampling distributions.This paper gives an overview of the salient progress of self-normalized limit theory, from Student's t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one-and two-sample U-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence.
【作者单位】Department
【关键词】Berry-Esseen inequality Hotelling's T-statistic large deviation moderate deviation self-normalization Student's t-statistic U-statistic
【基金】:Supported by Hong Kong RGC GRF 14302515
【分类号】:O21
【正文快照】:
§1 IntroductionAs one of the most important statistics,Student’s t-statistic[71]has a wide range of appli-cations in probability,statistics,finance and other fields of science.During the past century,the t-statistic has evolved into much more general S

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