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Biometrika 2007 94(4):977-984; doi:10.1093/biomet/asm068
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© 2007 Biometrika Trust

Miscellanea

Miscellanea Kernel-Type Density Estimation on the Unit Interval

M.C. Jones

Department of Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, U.K. m.c.jones{at}open.ac.uk

D.A. Henderson

School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. d.a.henderson{at}ncl.ac.uk

Received for publication 1 December 2006. Revision received 1 March 2007.
  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.

Key Words: Boundary behaviour • Copula • Kernel density estimation


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