Open Access
Translator Disclaimer
April 2004 A uniform functional law of the logarithm for the local empirical process
David M. Mason
Ann. Probab. 32(2): 1391-1418 (April 2004). DOI: 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.

Citation

Download Citation

David M. Mason. "A uniform functional law of the logarithm for the local empirical process." Ann. Probab. 32 (2) 1391 - 1418, April 2004. https://doi.org/10.1214/009117904000000243

Information

Published: April 2004
First available in Project Euclid: 18 May 2004

zbMATH: 1057.60029
MathSciNet: MR2060302
Digital Object Identifier: 10.1214/009117904000000243

Subjects:
Primary: 60F05 , 60F15 , 62E20 , 62G30

Keywords: consistency , empirical process , kernel density estimation , large deviations

Rights: Copyright © 2004 Institute of Mathematical Statistics

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.32 • No. 2 • April 2004
Back to Top