Open Access
Translator Disclaimer
May, 1984 The Bounded Law of the Iterated Logarithm for the Weighted Empirical Distribution Process in the Non-I.I.D. Case
Michael B. Marcus, Joel Zinn
Ann. Probab. 12(2): 335-360 (May, 1984). DOI: 10.1214/aop/1176993294

Abstract

Using a simple symmetrization procedure, an upper bound is obtained for the probability distribution of various kinds of weighted empirical distribution processes where the underlying real valued random variables are not identically distributed. These probability bounds are used to obtain bounded laws of the iterated logarithm for empirical processes with different kinds of weighting. They are also used to obtain a one sided version of Daniel's theorem in the non-i.i.d. case.

Citation

Download Citation

Michael B. Marcus. Joel Zinn. "The Bounded Law of the Iterated Logarithm for the Weighted Empirical Distribution Process in the Non-I.I.D. Case." Ann. Probab. 12 (2) 335 - 360, May, 1984. https://doi.org/10.1214/aop/1176993294

Information

Published: May, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0538.60009
MathSciNet: MR735842
Digital Object Identifier: 10.1214/aop/1176993294

Subjects:
Primary: 60B12
Secondary: 60F15 , 62F12 , 62F25

Keywords: Daniel's theorem , Empirical distribution process , Law of the iterated logarithm

Rights: Copyright © 1984 Institute of Mathematical Statistics

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.12 • No. 2 • May, 1984
Back to Top