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

Authors
DEHEUVELS P MASON DM
Citation
P. Deheuvels et Dm. Mason, FUNCTIONAL LAWS OF THE ITERATED LOGARITHM FOR LOCAL EMPIRICAL PROCESSES INDEXED BY SETS, Annals of probability, 22(3), 1994, pp. 1619-1661
Citations number
35
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
22
Issue
3
Year of publication
1994
Pages
1619 - 1661
Database
ISI
SICI code
0091-1798(1994)22:3<1619:FLOTIL>2.0.ZU;2-#
Abstract
We introduce the notion of a multivariate local (and tail) empirical p rocess indexed by sets and establish a number of functional laws of th e iterated logarithm for such processes. This leads to a unified metho dology to study the almost sure behavior of various statistics which a re local functionals of the empirical distribution. Such statistics in clude density estimators and the Bahadur-Kiefer representation.