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A minimax result for a class of nonparametric density estimators


Engel, Joachim; Gasser, Theo (1995). A minimax result for a class of nonparametric density estimators. Journal of Nonparametric Statistics, 4(4):327-334.

Abstract

A class of kernel type density estimators with locally varying bandwidth is introduced. This class contains the fixed bandwidth estimator, the nearest neighbor estimator, the penalized maximum likelihood estimator and a variance stabilizing estimator. While based on asymptotic mean integrated square error (AMISE), there is no uniformly optimal method, the fixed bandwidth estimator is minimax optimal.

Abstract

A class of kernel type density estimators with locally varying bandwidth is introduced. This class contains the fixed bandwidth estimator, the nearest neighbor estimator, the penalized maximum likelihood estimator and a variance stabilizing estimator. While based on asymptotic mean integrated square error (AMISE), there is no uniformly optimal method, the fixed bandwidth estimator is minimax optimal.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Uncontrolled Keywords:Nonparametric density estimation, kernel methods, nearest neighbor estimator, penalized maximum likelihood estimator, variance stabilizing, minimax optimality
Language:English
Date:1995
Deposited On:26 May 2016 19:36
Last Modified:26 May 2016 19:36
Publisher:Taylor & Francis
ISSN:1026-7654
Publisher DOI:https://doi.org/10.1080/10485259508832624

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