A refined randomized concentration inequality

Lei，Xiaoyu1; Shao，Qi Man2

2022-08-01

10.1016/j.spl.2022.109513

STATISTICS & PROBABILITY LETTERS   影响因子和分区

0167-7152

1879-2103

Let xi(1), xi(2), ..., xi(n) be independent random variables with E xi(i) = 0 and Sigma(n)(i=1) E xi(2)(i) = 1 and let Delta = Delta(xi(1), ..., xi(n)) Set W = Sigma(n)(i=1) xi(i). In this note we prove that vertical bar P(W <= Delta) - E Phi(Delta)vertical bar <= 36 Sigma(n)(i=1) E xi(2)(i) min(1, vertical bar xi(i)vertical bar)+24 Sigma(n)(i=1) parallel to xi(i)parallel to(2)parallel to Delta - Delta((i))parallel to 2, where Delta((i)) is any random variable that doesn't depend on xi(i). The result leads to a refined Berry-Esseen inequality for non-linear statistics W + Delta as well as a refined concentration inequality for P(W <= Delta(2)) - P(W <= Delta(1)). (C) 2022 Elsevier B.V. All rights reserved.

Randomized concentration inequality Berry-Esseen bounds Non-linear statistics Stein's method

SCI

英语

其他

National Nature Science Foundation of China NSFC[12031005]

Mathematics

Statistics & Probability

WOS:000832995500001

ELSEVIER

2-s2.0-85129964911

Web of Science

1.Department of Statistics,The University of Chicago,Chicago,60615,United States
2.Department of Statistics and Data Science,SICM,National Center for Applied Mathematics Shenzhen,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Lei，Xiaoyu,Shao，Qi Man. A refined randomized concentration inequality[J]. STATISTICS &amp; PROBABILITY LETTERS,2022,187.

Lei，Xiaoyu,&Shao，Qi Man.(2022).A refined randomized concentration inequality.STATISTICS & PROBABILITY LETTERS,187.

Lei，Xiaoyu,et al."A refined randomized concentration inequality".STATISTICS & PROBABILITY LETTERS 187(2022).