The Annals of Probability

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

David M. Mason

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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.

Article information

Source
Ann. Probab., Volume 32, Number 2 (2004), 1391-1418.

Dates
First available in Project Euclid: 18 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1084884855

Digital Object Identifier
doi:10.1214/009117904000000243

Mathematical Reviews number (MathSciNet)
MR2060302

Zentralblatt MATH identifier
1057.60029

Subjects
Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 62E20: Asymptotic distribution theory 62G30: Order statistics; empirical distribution functions

Keywords
Empirical process kernel density estimation consistency large deviations

Citation

Mason, David M. A uniform functional law of the logarithm for the local empirical process. Ann. Probab. 32 (2004), no. 2, 1391--1418. doi:10.1214/009117904000000243. https://projecteuclid.org/euclid.aop/1084884855


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