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November 2011 Uniform bounds for norms of sums of independent random functions
Alexander Goldenshluger, Oleg Lepski
Ann. Probab. 39(6): 2318-2384 (November 2011). DOI: 10.1214/10-AOP595

Abstract

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the ${\mathbb{L}}_{s}$-norms of empirical and regression-type processes. Usefulness of the obtained results is illustrated by application to the processes appearing in kernel density estimation and in nonparametric estimation of regression functions.

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Alexander Goldenshluger. Oleg Lepski. "Uniform bounds for norms of sums of independent random functions." Ann. Probab. 39 (6) 2318 - 2384, November 2011. https://doi.org/10.1214/10-AOP595

Information

Published: November 2011
First available in Project Euclid: 17 November 2011

zbMATH: 1238.60023
MathSciNet: MR2932670
Digital Object Identifier: 10.1214/10-AOP595

Subjects:
Primary: 60E15
Secondary: 62G07 , 62G08

Keywords: Concentration inequalities , Empirical processes , kernel density estimation , regression

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 6 • November 2011
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