## The Annals of Statistics

### An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation

James Stephen Marron

#### Abstract

A data-driven method of choosing the bandwidth, $h$, of a kernel density estimator is heuristically motivated by considering modifications of the Kullback-Leibler or pseudo-likelihood cross-validation function. It is seen that this means of choosing $h$ is asymptotically equivalent to taking the $h$ that minimizes some compelling error criteria such as the average squared error and the integrated squared error. Thus, for a given kernel function, the bandwidth can be chosen optimally without making precise smoothness assumptions on the underlying density.

#### Article information

Source
Ann. Statist., Volume 13, Number 3 (1985), 1011-1023.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349653

Digital Object Identifier
doi:10.1214/aos/1176349653

Mathematical Reviews number (MathSciNet)
MR803755

Zentralblatt MATH identifier
0585.62073

JSTOR