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VOL. 5 | 2009 Uniform Central Limit Theorems for pregaussian classes of functions

## Abstract

We study weak convergence of general (smoothed) empirical processes indexed by classes of functions $\mathcal{F}$ under minimal conditions. We present a general result that, applied to specific situations, enables us to prove uniform central limit theorems under P-pregaussian assumption on $\mathcal{F}$ only.

## Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60026
MathSciNet: MR2797942

Digital Object Identifier: 10.1214/09-IMSCOLL507

Keywords: Empirical processes , Fourier series density estimator , kernel density estimator , uniform central limit theorems , weak convergence