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Miscellanea kernel-type density estimation on the unit interval

Lookup NU author(s): Dr Daniel Henderson

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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. © 2007 Biometrika Trust.


Publication metadata

Author(s): Jones MC, Henderson DA

Publication type: Article

Publication status: Published

Journal: Biometrika

Year: 2007

Volume: 94

Issue: 4

Pages: 977-984

ISSN (print): 0006-3444

ISSN (electronic): 1464-3510

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/biomet/asm068

DOI: 10.1093/biomet/asm068


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