A CLT FOR EMPIRICAL PROCESSES INVOLVING TIME-DEPENDENT DATA

被引：9

作者：

Kuelbs, James ^{[1
]}

Kurtz, Thomas ^{[1
]}

Zinn, Joel ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77840 USA

来源：

ANNALS OF PROBABILITY | 2013年 / 41卷 / 02期

基金：

美国国家科学基金会;

关键词：

Central limit theorems; empirical processes; LIMIT-THEOREMS; CONVERGENCE;

D O I：

10.1214/11-AOP711

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：

For stochastic processes {X-t : t is an element of E}, we establish sufficient conditions for the empirical process based on {I-Xt <= y - Pr(X-t <= y) : t is an element of E, y is an element of R} to satisfy the CLT uniformly in t is an element of E, y is an element of R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E = [0, 1].

引用

页码：785 / 816

页数：32

共 19 条

[1] THE CENTRAL LIMIT-THEOREM AND THE LAW OF ITERATED LOGARITHM FOR EMPIRICAL PROCESSES UNDER LOCAL CONDITIONS [J].