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

2004/10/06 by David M. Mason
Mathematics · #math.PR #msc:60F05 #msc:60F15 #msc:62E20 #msc:62G30

paper · pdf · doi:10.1214/009117904000000243

published as Annals of Probability 2004, Vol. 32, No. 2, 1391-1418 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000243

arxiv created 2004/10/06 · arxiv updated 2009/12/01

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.

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