I. G. Shevtsova, “A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums”, Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 2,Pages <nobr>345

This article is cited in 7 papers

A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums

I. G. Shevtsova^abc

^a Hangzhou Dianzi University, Zhejiang
^b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
^c Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: A moment inequality between the central and noncentral third-order absolute moments is proved, which is optimal for every value of the recentering parameter. By use of this inequality there are constructed convergence rate estimates in the central limit theorem for Poisson-binomial random sums in the uniform and mean metrics.

Keywords: compound Poisson-binomial distribution, central limit theorem (CLT), convergence rate estimate, normal approximation, Berry– Esséen inequality, moment inequality.

Received: 15.09.2016
Accepted: 23.02.2017

DOI: 10.4213/tvp5097