Asymptotic development for the CLT in total variation distance

被引：14

作者：

Bally, Vlad ^{[1
]}

Caramellino, Lucia ^{[2
]}

机构：

[1] Univ Paris Est, UPEC, UPEMLV, MathRisk INRIA,LAMA UMR CNRS, F-77454 Marne La Vallee, France

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

来源：

BERNOULLI | 2016年 / 22卷 / 04期

关键词：

abstract Malliavin calculus; integration by parts; regularizing functions; total variation distance; BERRY-ESSEEN BOUNDS;

D O I：

10.3150/15-BEJ734

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：

The aim of this paper is to study the asymptotic expansion in total variation in the central limit theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely continuous component): we develop the error in powers of n(-1/2) and give an explicit formula for the approximating measure.

引用

页码：2442 / 2485

页数：44

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