The Annals of Statistics

An Application of the Efron-Stein Inequality in Density Estimation

Luc Devroye

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.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1317-1320.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350508

Digital Object Identifier
doi:10.1214/aos/1176350508

Mathematical Reviews number (MathSciNet)
MR902261

Zentralblatt MATH identifier
0631.62039

JSTOR