Necessary and sufficient conditions for weak convergence of smoothed empirical processes

被引：6

作者：

Radulovic, D ^{[1
]}

Wegkamp, M ^{[1
]}

机构：

[1] Yale Univ, Dept Stat, New Haven, CT 06520 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2003年 / 61卷 / 03期

关键词：

bracketing numbers; empirical processes; Hellinger differentiability; histogram estimators; metric entropy; weak convergence;

D O I：

10.1016/S0167-7152(02)00395-4

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：

Let X1,...,Xn be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator P,,H and establish weak convergence of the empirical process rootn-(P-n,P-H -P)(f)(f is an element of f) under sharp conditions. If F is a class of indicators of sets, then the conditions imposed are necessary and sufficient. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：321 / 336

页数：16

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