分布的伯恩斯坦型界

IF 0.7 Q3 STATISTICS & PROBABILITY

Modern Stochastics-Theory and Applications Pub Date : 2021-01-06 DOI:10.15559/23-vmsta223

M. Skorski

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引用次数: 10

摘要

这项工作为无处不在的beta分布获得了Bernstein型的尖锐闭型指数浓度不等式，改进了先前在此背景下研究的亚高斯和亚伽马边界。这个证明利用了一种新的方便的2阶递归来处理beta分布的中心矩，它是从矩的超几何表示中得到的;这种递归对于获得中心矩和各种尾部近似的显式表达式是有用的。

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Bernstein-type bounds for beta distribution

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations.

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来源期刊

Modern Stochastics-Theory and Applications STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

50.00%

发文量

审稿时长

10 weeks