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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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