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Media type:
E-Article
Title:
Gaussian Characterization of Uniform Donsker Classes of Functions
Contributor:
Gine, Evarist;
Zinn, Joel
imprint:
Institute of Mathematical Statistics, 1991
Published in:The Annals of Probability
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
<p>It is proved that, for classes of functions F satisfying some measurability, the empirical processes indexed by F and based on P ∈ P(S) satisfy the central limit theorem uniformly in P ∈ P(S) if and only if the P-Brownian bridges G<sub>p</sub>indexed by F are sample bounded and ρ<sub>p</sub>uniformly continuous uniformly in P ∈ P(S). Uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions are also obtained.</p>