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September, 1987 An Application of the Efron-Stein Inequality in Density Estimation
Luc Devroye
Ann. Statist. 15(3): 1317-1320 (September, 1987). DOI: 10.1214/aos/1176350508

Abstract

The Efron-Stein inequality is applied to prove that the kernel density estimate $f_n$, with an arbitrary nonnegative kernel and an arbitrary smoothing factor, satisfies the inequality $\operatorname{var}(\int|f_n - f|) \leq 4/n$ for all densities $f$. Similar inequalities are obtained for other estimates.

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Luc Devroye. "An Application of the Efron-Stein Inequality in Density Estimation." Ann. Statist. 15 (3) 1317 - 1320, September, 1987. https://doi.org/10.1214/aos/1176350508

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0631.62039
MathSciNet: MR902261
Digital Object Identifier: 10.1214/aos/1176350508

Subjects:
Primary: 60E15
Secondary: 62G05

Keywords: Density estimation , distribution-free confidence interval , Efron-Stein inequality , kernel estimate

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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