Rates of convergence for minimal distances in the central limit theorem under projective criteria

被引：20

作者：

Dedecker, Jerome ^{[1
]}

Merlevede, Florence ^{[2
]}

Rio, Emmanuel ^{[3
]}

机构：

[1] Univ Paris 06, LSTA, F-75013 Paris, France

[2] Univ Paris Est, CNRS, Math Lab, UMR 8050, F-77435 Champs Sur Marne, France

[3] Univ Versailles, CNRS, Math Lab, UMR 8100, F-78035 Versailles, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

关键词：

Minimal and ideal distances; rates of convergence; Martingale difference sequences; stationary sequences; projective criteria; weak dependence; uniform mixing;

D O I：

10.1214/EJP.v14-648

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：

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

引用

页码：978 / 1011

页数：34

共 22 条

[1]

[Anonymous], 1989, REAL ANAL PROBABILIT

[2]

Broise A, 1996, ASTERISQUE, P1

[3]

Davydov Y., 1973, Theory of Probability and its Applications, VXVIII, P312

[4] On mean central limit theorems for stationary sequences [J].

Dedecker, Jerome ;

Rio, Emmanuel .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (04) :693-726

[5] An empirical central limit theorem for dependent sequences [J].

Dedecker, Jerome ;

Prieur, Clementine .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (01) :121-142

[6]

FRECHET M, 1957, CR HEBD ACAD SCI, V244, P689

[7]

GORDIN MI, 1969, DOKL AKAD NAUK SSSR+, V188, P739

[8]

HEYDE CC, 1970, ANN MATH STAT, V41, P2161, DOI 10.1214/aoms/1177696722

[9] ON ACCURACY OF GAUSSIAN APPROXIMATION TO DISTRIBUTION FUNCTIONS OF SUMS OF INDEPENDENT VARIABLES [J].

IBRAGIMOV, IA .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1966, 11 (04) :559-+

[10]

JAN C, 2001, THESIS U RENNES 1

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