The Annals of Statistics

Asymptotic Performance Bounds for the Kernel Estimate

Luc Devroye

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Abstract

We consider an arbitrary sequence of kernel density estimates $f_n$ with kernels $K_n$ possibly depending upon $n$. Under a mild restriction on the sequence $K_n$, we obtain inequalities of the type $E\big(\int|f_n - f|\big) \geq (1 + o(1))\Psi(n, f),$ where $f$ is the density being estimated and $\Psi(n, f)$ is a function of $n$ and $f$ only. The function $\psi$ can be considered as an indicator of the difficulty of estimating $f$ with any kernel estimate.

Article information

Source
Ann. Statist., Volume 16, Number 3 (1988), 1162-1179.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350953

Digital Object Identifier
doi:10.1214/aos/1176350953

Mathematical Reviews number (MathSciNet)
MR959194

Zentralblatt MATH identifier
0671.62041

JSTOR
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62G05: Estimation

Keywords
Density estimation $L_1$ error inequalities characteristic function kernel estimate performance bounds

Citation

Devroye, Luc. Asymptotic Performance Bounds for the Kernel Estimate. Ann. Statist. 16 (1988), no. 3, 1162--1179. doi:10.1214/aos/1176350953. https://projecteuclid.org/euclid.aos/1176350953


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