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Kernel-type density estimation on the unit interval

Jones, M. C. and Henderson, D. A. (2007). Kernel-type density estimation on the unit interval. Biometrika, 94(4) pp. 977–984.

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DOI (Digital Object Identifier) Link: http://doi.org/10.1093/biomet/asm068
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Abstract

We consider kernel-type methods for the estimation of a density on 0,1 which eschew explicit boundary correction. We propose using kernels that are symmetric in their two arguments; these kernels are conditional densities of bivariate copulas. We give asymptotic theory for the version of the new estimator using Gaussian copula kernels and report on simulation comparisons of it with the beta-kernel density estimator of Chen ([1]). We also provide automatic bandwidth selection in the form of 'rule-of-thumb' bandwidths for both estimators. As well as its competitive integrated squared error performance, advantages of the new approach include its greater range of possible values at 0 and 1, the fact that it is a bona fide density and that the individual kernels and resulting estimator are comprehensible in terms of a single simple picture.

Item Type: Journal Article
Copyright Holders: 2007 Biometrika Trust
ISSN: 1464-3510
Keywords: boundary behaviour; copula; kernel density estimation
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 22541
Depositing User: Sarah Frain
Date Deposited: 19 Aug 2010 12:38
Last Modified: 24 Feb 2016 10:07
URI: http://oro.open.ac.uk/id/eprint/22541
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