Asymptotics for sums of a function of normalized independent sums

被引：2

作者：

Kosinski, Kamil ^{[1
]}

机构：

[1] Univ Warsaw, Wydzial Matemat Informart & Mech, Warsaw, Poland

来源：

STATISTICS & PROBABILITY LETTERS | 2009年 / 79卷 / 04期

关键词：

PRODUCTS;

D O I：

10.1016/j.spl.2008.09.013

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：

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular, we show that previously known result from Rempala and Wesolowski [Rempala, G., Wesolowski, J., 2005. Asymptotics for products of independent sums with an application to Wishart determinants. Statist. Probab. Lett. 74 129-138], which can be obtained by applying the logarithm as the function, holds true under weaker assumptions. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：415 / 419

页数：5

共 7 条

[1]

Hall P, 1980, Martingale Limit Theory and Its Applications

[2] COMPLETE CONVERGENCE AND THE LAW OF LARGE NUMBERS [J].

HSU, PL ;

ROBBINS, H .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1947, 33 (02) :25-31

[3] COMPLETE CONVERGENCE AND ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM-VARIABLES [J].

LI, DL ;

RAO, MB ;

JIANG, TF ;

WANG, XC .

JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (01) :49-76

[4] A note on asymptotic distribution of products of sums [J].

Lu, XW ;

Qi, YC .

STATISTICS & PROBABILITY LETTERS, 2004, 68 (04) :407-413

[5] Limit distributions for products of sums [J].

Qi, YC .

STATISTICS & PROBABILITY LETTERS, 2003, 62 (01) :93-100

[6] Asymptotics for products of independent sums with an application to Wishart determinants [J].

Rempala, G ;

Wesolowski, J .

STATISTICS & PROBABILITY LETTERS, 2005, 74 (02) :129-138

[7] ASYMPTOTICS FOR PRODUCTS OF SUMS AND U-STATISTICS [J].

Rempala, Grzegorz ;

Wesolowski, Jacek .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2002, 7 :47-54

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