Uniform bounds for norms of sums of independent random functions

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.

Published in at http://dx.doi.org/10.1214/10-AOP595 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Risk hull method and regularization by projections of ill-posed inverse problems
• Universal pointwise selection rule in multivariate function estimation

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