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Uniform central limit theorems for sieved maximum likelihood and trigonometric series estimators on the unit circle

Richard Nickl

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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.

Chapter information

Source
Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 338-356

Dates
First available in Project Euclid: 2 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1265119278

Digital Object Identifier
doi:10.1214/09-IMSCOLL522

Mathematical Reviews number (MathSciNet)
MR2797957

Zentralblatt MATH identifier
1243.60031

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
density estimation orthogonal series estimator sieved maximum likelihood estimator uniform central limit theorem

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

Nickl, Richard. Uniform central limit theorems for sieved maximum likelihood and trigonometric series estimators on the unit circle. High Dimensional Probability V: The Luminy Volume, 338--356, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-IMSCOLL522. https://projecteuclid.org/euclid.imsc/1265119278


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