FUNCTIONAL LAWS OF THE ITERATED LOGARITHM FOR LOCAL EMPIRICAL PROCESSES INDEXED BY SETS

被引：29

作者：

DEHEUVELS, P ^{[1
]}

MASON, DM ^{[1
]}

机构：

[1] UNIV DELAWARE,DEPT MATH SCI,NEWARK,DE 19716

来源：

ANNALS OF PROBABILITY | 1994年 / 22卷 / 03期

关键词：

EMPIRICAL MEASURES; STRONG LAWS; FUNCTIONAL LAWS OF THE ITERATED LOGARITHM; DONSKER CLASSES; TAIL EMPIRICAL PROCESSES; DENSITY ESTIMATION; BAHADUR-KIEFER REPRESENTATION;

D O I：

10.1214/aop/1176988617

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 introduce the notion of a multivariate local (and tail) empirical process indexed by sets and establish a number of functional laws of the iterated logarithm for such processes. This leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution. Such statistics include density estimators and the Bahadur-Kiefer representation.

引用

页码：1619 / 1661

页数：43

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[1] THE CENTRAL-LIMIT-THEOREM FOR EMPIRICAL PROCESSES ON VAPNIK-CERVONENKIS CLASSES [J].