Berry-Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances

被引：15

作者：

Bobkov, Sergey G. ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, 127 Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2018年 / 170卷 / 1-2期

关键词：

Central limit theorem; Transport distances; Edgeworth expansions; Coupling; MINIMAL DISTANCES; CONSTANTS;

D O I：

10.1007/s00440-017-0756-2

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：

For sums of independent random variables , Berry-Esseen-type bounds are derived for the power transport distances in terms of Lyapunov coefficients . In the case of identically distributed summands, the rates of convergence are refined under Cram,r's condition.

引用

页码：229 / 262

页数：34

共 37 条

[1] GLOBAL VERSIONS OF THE CENTRAL LIMIT THEOREM [J].

AGNEW, RP .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1954, 40 (09) :800-804

[2] ASYMPTOTIC EXPANSIONS IN GLOBAL CENTRAL LIMIT-THEOREMS [J].

AGNEW, RP .

ANNALS OF MATHEMATICAL STATISTICS, 1959, 30 (03) :721-737

[3] ESTIMATES FOR GLOBAL CENTRAL LIMIT-THEOREMS [J].

AGNEW, RP .

ANNALS OF MATHEMATICAL STATISTICS, 1957, 28 (01) :26-42

[4]

[Anonymous], LIMIT THEOREMS PROBA

[5]

[Anonymous], 1949, AM MATH SOC

[6]

[Anonymous], VESTNIK LENINGRAD U

[7]

Bartfai P, 1970, Studia Sci. Math. Hungar, V5, P41

[8] DUALITY FOR BOREL MEASURABLE COST FUNCTIONS [J].

Beiglboeck, Mathias ;

Schachermayer, Walter .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (08) :4203-4224

[9]

Bhattacharya R.N., 1976, Normal Approximation and Asymptotic Expansions

[10]

Bikjalis A., 1973, MATH STAT PROBABILIT, V7, P149

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