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arXiv · 0904.1950

Uniform bounds for norms of sums of independent random functions

Alexander Goldenshluger·Oleg Lepski
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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. 2009-04-13. Uniform bounds for norms of sums of independent random functions. https://doi.org/10.1214/10-aop595

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