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April, 1989 Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes
M. Ledoux, M. Talagrand
Ann. Probab. 17(2): 596-631 (April, 1989). DOI: 10.1214/aop/1176991418

Abstract

In this paper, we obtain several new results and developments in the study of empirical processes. A comparison theorem for Rademacher averages is at the basis of the first part of the results, with applications, in particular, to Kolmogorov's law of the iterated logarithm and Prokhorov's law of large numbers for empirical processes. We then study the behavior of empirical processes along a class of functions through random geometric conditions and complete in this way the characterization of the law of the iterated logarithm. Bracketing and local Lipschitz conditions provide illustrations of some of these ideas to concrete situations.

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M. Ledoux. M. Talagrand. "Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes." Ann. Probab. 17 (2) 596 - 631, April, 1989. https://doi.org/10.1214/aop/1176991418

Information

Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0679.60048
MathSciNet: MR985381
Digital Object Identifier: 10.1214/aop/1176991418

Subjects:
Primary: 60F17
Secondary: 60B12 , 60F05

Keywords: comparison theorems , Empirical processes , limit theorems , Random geometry

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • April, 1989
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