The Annals of Statistics

On Good Deterministic Smoothing Sequences for Kernel Density Estimates

Luc Devroye

Full-text: Open access

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, $\operatornamewithlimits{\lim\inf}_{n\rightarrow\infty} \frac{\mathbf{E} \int |f_{nh_n} - f|}{\inf_h \mathbf{E} \int |f_{nh} - f|} = 1.$

Article information

Source
Ann. Statist., Volume 22, Number 2 (1994), 886-889.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325500

Digital Object Identifier
doi:10.1214/aos/1176325500

Mathematical Reviews number (MathSciNet)
MR1292545

Zentralblatt MATH identifier
0805.62039

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62G05: Estimation 62F12: Asymptotic properties of estimators 60F25: $L^p$-limit theorems

Keywords
Density estimation kernel estimate probabilistic method nonparametric methods smoothing

Citation

Devroye, Luc. On Good Deterministic Smoothing Sequences for Kernel Density Estimates. Ann. Statist. 22 (1994), no. 2, 886--889. doi:10.1214/aos/1176325500. https://projecteuclid.org/euclid.aos/1176325500


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