On optimal data-based bandwidth selection in kernel density estimation

Hall, Peter; Sheather, Simon J.; Jones, M. C. and Marron, J. S (1991). On optimal data-based bandwidth selection in kernel density estimation. Biometrika, 78(2) pp. 263–269.

DOI: https://doi.org/10.1093/biomet/78.2.263

Abstract

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^−½ where n → ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

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