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December 1996 A universally acceptable smoothing factor for kernel density estimates
Luc Devroye, Gábor Lugosi
Ann. Statist. 24(6): 2499-2512 (December 1996). DOI: 10.1214/aos/1032181164


We define a minimum distance estimate of the smoothing factor for kernel density estimates, based on a methodology first developed by Yatracos. It is shown that if $f_{nh}$ denotes the kernel density estimate on $\mathbb{R}^d$ for an i.i.d. sample of size n drawn from an unknown density f, where h is the smoothing factor, and if $f_n$ is the kernel estimate with the same kernel and with the proposed new data-based smoothing factor, then, under a regularity condition on the kernel K, $$\sup_f \limsup_{n \to \infty} \frac{E \int | f_n - f|dx}{\inf_{h>0} E \int |f_{nh} - f|dx} \leq 3.$$ This is the first published smoothing factor that can be proven to have this property.


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Luc Devroye. Gábor Lugosi. "A universally acceptable smoothing factor for kernel density estimates." Ann. Statist. 24 (6) 2499 - 2512, December 1996.


Published: December 1996
First available in Project Euclid: 16 September 2002

zbMATH: 0867.62024
MathSciNet: MR1425963
Digital Object Identifier: 10.1214/aos/1032181164

Primary: 62G05

Keywords: asymptotic optimality , convergence , Density estimation , kernel estimate , minimum distance estimate , smoothing factor

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 1996
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