Abstract
Given an i.i.d. sample from the law ℙ on the unit circle, we obtain uniform central limit theorems for the random measures induced by trigonometric series and sieved maximum likelihood density estimators. The limit theorems are uniform over balls in Sobolev-Hilbert spaces of order s>1/2.
Information
Published: 1 January 2009
First available in Project Euclid: 2 February 2010
zbMATH: 1243.60031
MathSciNet: MR2797957
Digital Object Identifier: 10.1214/09-IMSCOLL522
Subjects:
Primary:
60F17
Secondary:
46E35
Keywords:
Density estimation
,
orthogonal series estimator
,
sieved maximum likelihood estimator
,
uniform central limit theorem
Rights: Copyright © 2009, Institute of Mathematical Statistics
