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Article Dans Une Revue Annals of Probability Année : 2011

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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Dates et versions

hal-01265260 , version 1 (02-02-2016)

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Alexander Goldenshluger, Oleg Lepski. UNIFORM BOUNDS FOR NORMS OF SUMS OF INDEPENDENT RANDOM FUNCTIONS. Annals of Probability, 2011, 39 (6), pp.2318-2384. ⟨10.1214/10-AOP595⟩. ⟨hal-01265260⟩
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