A uniform functional law of the logarithm for the local empirical process

Preprint

6 October 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0410143

Abstract

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.

Keywords

CONSISTENCY OF D VARIATE
NONPARAMETRIC FUNCTION
UNIFORM FUNCTIONAL LAW
STRONG CONSISTENCY
ABSTRACT EMPIRICAL
EMPIRICAL PROCESS
LOCAL EMPIRICAL

All Related Versions

Version 1, 2004-10-06, ArXiv
Published version: The Annals of Probability, 32 (2), 1391.

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