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Biometrika 1991 78(2):263-269; doi:10.1093/biomet/78.2.263
© 1991 by Biometrika Trust
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On optimal data-based bandwidth selection in kernel density estimation

PETER HALL1, SIMON J. SHEATHER2, M. C. JONES3 and J. S. MARRON4

1Department of Statistics, Australian National University Canberra, ACT 2601, Australia
2Australian Graduate School of Management, University of New South Wales Kensington, NSW 2033, Australia
3Department of Statistics, The Open University Milton Keynes, MK7 6AA, U.K.
4Department of Statistics, University of North Carolina Chapel Hill, NC 27599–3260, U.S.A.

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n–1/2 where n {uparrow} {infty} denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

Key Words: Adaptive procedure • Convergence rate • Functional estimation • Mean integrated squared error • Smoothing parameter • Taylor expansion • Window width


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