The Annals of Probability

The Bounded Law of the Iterated Logarithm for the Weighted Empirical Distribution Process in the Non-I.I.D. Case

Michael B. Marcus and Joel Zinn

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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.

Article information

Source
Ann. Probab., Volume 12, Number 2 (1984), 335-360.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993294

Digital Object Identifier
doi:10.1214/aop/1176993294

Mathematical Reviews number (MathSciNet)
MR735842

Zentralblatt MATH identifier
0538.60009

JSTOR
links.jstor.org

Subjects
Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60F15: Strong theorems 62F25: Tolerance and confidence regions 62F12: Asymptotic properties of estimators

Keywords
Empirical distribution process law of the iterated logarithm Daniel's theorem

Citation

Marcus, Michael B.; Zinn, Joel. The Bounded Law of the Iterated Logarithm for the Weighted Empirical Distribution Process in the Non-I.I.D. Case. Ann. Probab. 12 (1984), no. 2, 335--360. doi:10.1214/aop/1176993294. https://projecteuclid.org/euclid.aop/1176993294


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