## Uniform central limit theorems for pregaussian classes of functions.(English)Zbl 1243.60026

Houdré, Christian (ed.) et al., High dimensional probability. V: The Luminy volume. Most papers based on the presentations at the conference (HDP V), Luminy, France, May 26–30, 2008. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-78-2). Institute of Mathematical Statistics Collections 5, 84-102 (2009).
Summary: 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.
For the entire collection see [Zbl 1228.60006].

### MSC:

 60F05 Central limit and other weak theorems 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference
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