A Uniform Functional Law of the Logarithm for the Local Empirical Process

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 us...

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Veröffentlicht in:	The Annals of probability 2004-04, Vol.32 (2), p.1391-1418
1. Verfasser:	Mason, David M.
Format:	Artikel
Sprache:	eng
Schlagworte:	60F05 60F15 62E20 62G30 Approximation consistency Consistent estimators Density estimation Distribution theory Empirical process Estimation methods Estimation theory Estimators Exact sciences and technology kernel density estimation large deviations Limit theorems Logarithms Mathematical analysis Mathematical functions Mathematics Nonparametric inference Normal distribution Probability Probability and statistics Probability theory and stochastic processes Random variables Sciences and techniques of general use Statistics Studies Uniform laws
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Beschreibung
Zusammenfassung:	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.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/009117904000000243