On Newman's central limit theorem

被引：1

作者：

Shashkin, A. P. ^{[1
]}

机构：

[1] MSU, Dept Probabil Theory, Moscow 119992, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2006年 / 50卷 / 02期

关键词：

associated random variables; stationarity; central limit theorem; slowly varying functions;

D O I：

10.1137/S0040585X97981731

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 construct an example of a strictly stationary associated random sequence which does not satisfy the central limit theorem and whose partial sums' variance grows in a defined regular way. This result generalizes the well-known example of N. Herrndorf and shows the optimality of conditions in the classical Newman's theorem.

引用

页码：330 / 337

页数：8

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