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
Rights: Copyright © 2009, Institute of Mathematical Statistics
