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December, 1984 The Consistency of Automatic Kernel Density Estimates
Luc Devroye, Clark S. Penrod
Ann. Statist. 12(4): 1231-1249 (December, 1984). DOI: 10.1214/aos/1176346789


We consider the Parzen-Rosenblatt kernel density estimate on $\mathbb{R}^d$ with data-dependent smoothing factor. Sufficient conditions on the asymptotic behavior of the smoothing factor are given under which the estimate is pointwise consistent almost everywhere for all densities $f$ to be estimated. When the smoothing factor is a function only of the sample size $n$, it is shown that these conditions are also necessary, a generalization of results by Deheuvels. The consistency of various automatic kernel density estimates is a simple consequence of these theorems.


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Luc Devroye. Clark S. Penrod. "The Consistency of Automatic Kernel Density Estimates." Ann. Statist. 12 (4) 1231 - 1249, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0569.62032
MathSciNet: MR760685
Digital Object Identifier: 10.1214/aos/1176346789

Primary: 60F15
Secondary: 62G05

Keywords: automatic kernel estimates , consistency , kernel density estimates , Nonparametric density estimation

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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