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

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

2004-10-06

arxiv.org/abs/math/0410143v1

Annals of Probability 2004, Vol. 32, No. 2, 1391-1418

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000243

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.

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