Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications

被引：1

作者：

Le Van Thanh ^{[1
]}

Nguyen Ngoc Tu ^{[2
,3
]}

机构：

[1] Vinh Univ, Dept Math, Vinh 42118, Nghe An, Vietnam

[2] HCMC Univ Technol & Educ, Dept Appl Sci, Linh Chieu Ward, 01 Vo Van Ngan, Ho Chi Minh City, Vietnam

[3] Ho Chi Minh City Natl Univ, Dept Math & Comp Sci, 227 Nguyen Van Cu,Dist 5, Ho Chi Minh City, Vietnam

来源：

ACTA MATHEMATICA VIETNAMICA | 2019年 / 44卷 / 04期

关键词：

Non-uniform Berry-Esseen bound; Coordinate symmetric random vector; Rate of convergence; Cone measure; Volume measure; CENTRAL-LIMIT-THEOREM; INEQUALITY; MARGINALS;

D O I：

10.1007/s40306-018-00305-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work establishes the nonuniform Berry-Esseen inequality for coordinate symmetric vectors. The nonuniform L-p (p >= 1) bound is also established. The main results are applied to projections of random vectors distributed according to a family of measures on the l(r)(n) sphere and the l(r)(n) ball, including cone measure and volume measure.

引用

页码：893 / 904

页数：12

共 50 条

[1] Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications
Le Van Thanh
Nguyen Ngoc Tu
[J]. Acta Mathematica Vietnamica, 2019, 44 : 893 - 904
[2] BERRY-ESSEEN BOUNDS FOR PROJECTIONS OF COORDINATE SYMMETRIC RANDOM VECTORS
Goldstein, Larry
Shao, Qi-Man
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2009, 14 : 474 - 485
[3] Non-uniform Berry-Esseen bounds for martingales with applications to statistical estimation
Fan, Xiequan
Grama, Ion
Liu, Quansheng
[J]. STATISTICS, 2017, 51 (01) : 105 - 122
[4] ON NON-UNIFORM BERRY-ESSEEN BOUNDS FOR TIME SERIES
Jirak, Moritz
[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2015, 35 (01): : 1 - 14
[5] Non-uniform and uniform Berry-Esseen type bounds for stationary associated sequences
Dewan, I
Rao, BLSP
[J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2005, 17 (02) : 217 - 235
[6] Non-uniform Berry-Esseen bound for U-statistics
Wang, QY
[J]. STATISTICA SINICA, 2002, 12 (04) : 1157 - 1169
[7] Anticoncentration and Berry-Esseen bounds for random tensors
Dodos, Pandelis
Tyros, Konstantinos
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2023, 187 (1-2) : 317 - 384
[8] Refinement on the Constants in the Non-Uniform Version of the Berry-Esseen Theorem
Thongtha, P.
Neammanee, K.
[J]. THAI JOURNAL OF MATHEMATICS, 2007, 5 (01): : 1 - 13
[9] A non-uniform Berry-Esseen bound via Stein's method
Chen, LHY
Shao, QM
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2001, 120 (02) : 236 - 254
[10] Non-uniform Berry-Esseen bound by unbounded exchangeable pairs approach
Da-li Liu
Zheng Li
Han-chao Wang
Zeng-jing Chen
[J]. Applied Mathematics-A Journal of Chinese Universities, 2021, 36 : 256 - 268

← 1 2 3 4 5 →