AN INTRODUCTION TO FUNCTIONAL CENTRAL LIMIT-THEOREMS FOR DEPENDENT STOCHASTIC-PROCESSES

被引：71

作者：

ANDREWS, DWK ^{[1
]}

POLLARD, D ^{[1
]}

机构：

[1] YALE UNIV,DEPT STAT,NEW HAVEN,CT 06520

来源：

INTERNATIONAL STATISTICAL REVIEW | 1994年 / 62卷 / 01期

关键词：

STRONG MIXING; FUNCTIONAL CENTRAL LIMIT THEOREM; EMPIRICAL PROCESS;

D O I：

10.2307/1403549

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：

This paper shows how the modern machinery for generating abstract empirical central limit theorems can be applied to arrays of dependent variables. It develops a bracketing approximation (closely related to results of Philipp and Massart) based on a moment inequality for sums of strong mixing arrays, in an effort to illustrate the sorts of difficulty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development are offered. The paper is largely self-contained.

引用

页码：119 / 132

页数：14

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