UNIFORM BOUNDS FOR NORMS OF SUMS OF INDEPENDENT RANDOM FUNCTIONS
Résumé
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 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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