## The Annals of Statistics

### On Good Deterministic Smoothing Sequences for Kernel Density Estimates

Luc Devroye

#### 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