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November, 1984 Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm
Kenneth S. Alexander
Ann. Probab. 12(4): 1041-1067 (November, 1984). DOI: 10.1214/aop/1176993141

Abstract

Sharp exponential bounds for the probabilities of deviations of the supremum of a (possibly non-iid) empirical process indexed by a class $\mathscr{F}$ of functions are proved under several kinds of conditions on $\mathscr{F}$. These bounds are used to establish laws of the iterated logarithm for this supremum and to obtain rates of convergence in total variation for empirical processes on the integers.

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Kenneth S. Alexander. "Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm." Ann. Probab. 12 (4) 1041 - 1067, November, 1984. https://doi.org/10.1214/aop/1176993141

Information

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

zbMATH: 0549.60024
MathSciNet: MR757769
Digital Object Identifier: 10.1214/aop/1176993141

Subjects:
Primary: 60F10
Secondary: 60F15 , 60G57

Keywords: empirical process , exponential bound , Law of the iterated logarithm , Metric entropy , Vapnik-Cervonenkis class

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 4 • November, 1984
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