Uniform bounds for norms of sums of independent random functions

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)2318-2384
Number of pages67
JournalAnnals of Probability
Issue number6
StatePublished - Nov 2011


  • Concentration inequalities
  • Empirical processes
  • Kernel density estimation
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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