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September, 1989 On the Relationship Between Stability of Extreme Order Statistics and Convergence of the Maximum Likelihood Kernel Density Estimate
Michel Broniatowski, Paul Deheuvels, Luc Devroye
Ann. Statist. 17(3): 1070-1086 (September, 1989). DOI: 10.1214/aos/1176347256

Abstract

Let $f$ be a density on the real line and let $f_n$ be the kernel estimate of $f$ in which the smoothing factor is obtained by maximizing the cross-validated likelihood product according to the method of Duin and Habbema, Hermans and Vandenbroek. Under mild regularity conditions on the kernel and $f$, we show, among other things that $\int|f_n - f| \rightarrow 0$ almost surely if and only if the sample extremes of $f$ are strongly stable.

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Michel Broniatowski. Paul Deheuvels. Luc Devroye. "On the Relationship Between Stability of Extreme Order Statistics and Convergence of the Maximum Likelihood Kernel Density Estimate." Ann. Statist. 17 (3) 1070 - 1086, September, 1989. https://doi.org/10.1214/aos/1176347256

Information

Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0701.62045
MathSciNet: MR1015138
Digital Object Identifier: 10.1214/aos/1176347256

Subjects:
Primary: 62G05

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • September, 1989
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