正态近似的累积量方法

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2021-02-02 DOI:10.1214/22-ps7
Hanna Doring, S. Jansen, K. Schubert
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引用次数: 12

摘要

这项调查致力于立陶宛概率学派对实值随机变量的正态近似得出的一系列著名的定量结果。关键成分是类型为|κj(X)|≤j的累积量上的一个界!1+γ/∆j−2,弱于有限指数矩的Cramér条件。我们在Saulis和Statulevičius(1989)的一本书中给出了一些“主要引理”的自成一体的证明,并对Cramér-Petrov系列进行了通俗易懂的介绍。此外,我们还解释了重尾威布尔变量、中等偏差和mod phi收敛的关系。我们讨论了一些边界累积量的方法,如混合累积量的可和性和依赖图,并简要回顾了累积量方法在正态近似中的一些最新应用。2020年数学学科分类:60F05;60F10;60G70;60K35。
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The method of cumulants for the normal approximation
The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable. The key ingredient is a bound on cumulants of the type |κj(X)| ≤ j!1+γ/∆j−2, which is weaker than Cramér’s condition of finite exponential moments. We give a self-contained proof of some of the “main lemmas” in a book by Saulis and Statulevičius (1989), and an accessible introduction to the Cramér-Petrov series. In addition, we explain relations with heavy-tailed Weibull variables, moderate deviations, and mod-phi convergence. We discuss some methods for bounding cumulants such as summability of mixed cumulants and dependency graphs, and briefly review a few recent applications of the method of cumulants for the normal approximation. Mathematics Subject Classification 2020: 60F05; 60F10; 60G70; 60K35.
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来源期刊
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
期刊最新文献
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