In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalit...In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalities developed by Chen and Shao[4,5]and can be applied to the quadratic forms and the general Curie-Weiss model.展开更多
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 tha...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.展开更多
An inequality describing the difference between Gamma and Gaussian distributions is derived. The asymptotic bound is much better than by existing uniform bound from Berry-Esseen inequality.
Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted ...Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted U-statistics and generalized L-statistic are established.展开更多
基金supported by National Key R&D Program of China(2018YFA0703900)the Na-tional Natural Science Foundation of China(11701331)+1 种基金Shandong Provincial Natural Science Founda-tion(ZR2017QA007)Young Slcholars Program of Shandong University。
文摘In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalities developed by Chen and Shao[4,5]and can be applied to the quadratic forms and the general Curie-Weiss model.
文摘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.
文摘An inequality describing the difference between Gamma and Gaussian distributions is derived. The asymptotic bound is much better than by existing uniform bound from Berry-Esseen inequality.
基金The research of Q.-M.Shao is partly supported by Hong Kong RGC GRF 603710,2130344.
文摘Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted U-statistics and generalized L-statistic are established.
