The Annals of Statistics

Exact Mean Integrated Squared Error

J. S. Marron and M. P. Wand

Full-text: Open access

Abstract

An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order. This provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis. The family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes. A number of applications of this method giving important new insights into kernel density estimation are presented. Among these is the discovery that the usual asymptotic approximations to the MISE can be quite inaccurate, especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 712-736.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348653

Digital Object Identifier
doi:10.1214/aos/1176348653

Mathematical Reviews number (MathSciNet)
MR1165589

Zentralblatt MATH identifier
0746.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 65D30: Numerical integration

Keywords
Gaussian-based kernel integrated squared error kernel estimator nonparametric density estimation normal mixture window width

Citation

Marron, J. S.; Wand, M. P. Exact Mean Integrated Squared Error. Ann. Statist. 20 (1992), no. 2, 712--736. doi:10.1214/aos/1176348653. https://projecteuclid.org/euclid.aos/1176348653


Export citation