A uniform functional law of the logarithm for the local empirical process
Open Access
- 1 April 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 32 (2) , 1391-1418
- https://doi.org/10.1214/009117904000000243
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
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