A MOMENT INEQUALITY WITH APPLICATION TO CONVERGENCE RATE ESTIMATES IN THE GLOBAL CLT FOR POISSON-BINOMIAL RANDOM SUMS

被引：4

作者：

Shevtsova, I. G. ^{[1
,2
,3
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou, Zhejiang, Peoples R China

[2] Russian Acad Sci, Fed Res Ctr Informat & Control, Inst Informat Problems, Moscow, Russia

[3] Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2018年 / 62卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

compound Poisson-binomial distribution; central limit theorem (CLT); convergence rate estimate; normal approximation; Berry-Esseen inequality; moment inequality; CENTRAL-LIMIT-THEOREM; NORMAL APPROXIMATION; ACCURACY;

D O I：

10.1137/S0040585X97T988605

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：278 / 294

页数：17

共 11 条

[1] CONVERGENCE RATE ESTIMATES IN THE GLOBAL CLT FOR COMPOUND MIXED POISSON DISTRIBUTIONS
Shevtsova, I. G.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2018, 63 (01) : 72 - 93
[2] On the Rate of Convergence in Limit Theorems for Negative-Binomial Random Sums
Hung, Tran Loc
Kien, Phan Tri
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2021, 42 (13) : 3127 - 3140
[3] ON THE RATE OF CONVERGENCE OF Lp NORMS IN THE CLT FOR POISSON AND GAMMA RANDOM VARIABLES
Sunklodas, J.
LITHUANIAN MATHEMATICAL JOURNAL, 2009, 49 (02) : 216 - 221
[4] On the rate of convergence of Lp norms in the CLT for poisson and gamma random variables
J. Sunklodas
Lithuanian Mathematical Journal, 2009, 49 : 216 - 221
[5] Bounds for convergence rate in laws of large numbers for mixed Poisson random sums
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Zeifman, Alexander
STATISTICS & PROBABILITY LETTERS, 2021, 168
[6] Structural Improvements of Nonuniform Convergence Rate Estimates in the Central Limit Theorem with Applications to Poisson Random Sums
Nefedova, Yu S.
Shevtsova, I. G.
DOKLADY MATHEMATICS, 2011, 84 (02) : 675 - 680
[7] Structural improvements of nonuniform convergence rate estimates in the central limit theorem with applications to poisson random sums
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Doklady Mathematics, 2011, 84 : 675 - 680
[8] On the rate of convergence in the global central limit theorem for random sums of independent random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2017, 57 (02) : 244 - 258
[9] On the rate of convergence in the global central limit theorem for random sums of independent random variables
Jonas Kazys Sunklodas
Lithuanian Mathematical Journal, 2017, 57 : 244 - 258
[10] On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables
Sunklodas, Jonas Kazys
LITHUANIAN MATHEMATICAL JOURNAL, 2020, 60 (03) : 410 - 423

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