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VOL. 51 | 2006 Oscillations of empirical distribution functions under dependence

Abstract

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as the one obtained under independence. The dependence conditions are expressed in terms of physical dependence measures which are directly related to the data-generating mechanism of the underlying processes and thus are easy to work with.

Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1126.60020
MathSciNet: MR2387760

Digital Object Identifier: 10.1214/074921706000000752

Subjects:
Primary: 60F05, 60G10
Secondary: 60G42

Rights: Copyright © 2006, Institute of Mathematical Statistics

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