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June, 1994 On Good Deterministic Smoothing Sequences for Kernel Density Estimates
Luc Devroye
Ann. Statist. 22(2): 886-889 (June, 1994). DOI: 10.1214/aos/1176325500

Abstract

We use the probabilistic method to show that if $f_{nh}$ is the standard kernel estimate with smoothing factor $h$, then there exists a deterministic sequence $h_n$ such that, for all densities, $\operatornamewithlimits{\lim\inf}_{n\rightarrow\infty} \frac{\mathbf{E} \int |f_{nh_n} - f|}{\inf_h \mathbf{E} \int |f_{nh} - f|} = 1.$

Citation

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Luc Devroye. "On Good Deterministic Smoothing Sequences for Kernel Density Estimates." Ann. Statist. 22 (2) 886 - 889, June, 1994. https://doi.org/10.1214/aos/1176325500

Information

Published: June, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0805.62039
MathSciNet: MR1292545
Digital Object Identifier: 10.1214/aos/1176325500

Subjects:
Primary: 62G07
Secondary: 60F25, 62F12, 62G05

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 2 • June, 1994
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