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Risk bounds for mixture density estimation

Published online by Cambridge University Press:  15 November 2005

Alexander Rakhlin ,
Dmitry Panchenko  and
Sayan Mukherjee
Alexander Rakhlin
Affiliation:
Center for Biological and Computational Learning, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; rakhlin@mit.edu
Dmitry Panchenko
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02143, USA.
Sayan Mukherjee
Affiliation:
Institute of Statistics and Decision Sciences, Institute for Genome Sciences and Policy, Duke University, Durham, NC 27708, USA.
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Abstract

In this paper we focus on the problem of estimating a boundeddensity using a finite combination of densities from a givenclass. We consider the Maximum Likelihood Estimator (MLE) and thegreedy procedure described by Li and Barron (1999)under the additional assumption of boundedness of densities. Weprove an $O(\frac{1}{\sqrt{n}})$ bound on the estimation errorwhich does not depend on the number of densities in the estimatedcombination. Under the boundedness assumption,this improves the bound of Li and Barron by removing the $\log n$ factor and also generalizes it to the base classes with convergingDudley integral.

Keywords

Mixture density estimationmaximum likelihoodRademacher processes.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 220 - 229
Copyright
© EDP Sciences, SMAI, 2005

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