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

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.

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

References in corpus (1)

• Uniform in bandwidth consistency of kernel-type function estimators

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• Oscillations of empirical distribution functions under dependence
• A law of the iterated logarithm for Grenander's estimator
• Central limit theorems for local empirical processes near boundaries of sets
• Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data