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June, 1992 Exact Mean Integrated Squared Error
J. S. Marron, M. P. Wand
Ann. Statist. 20(2): 712-736 (June, 1992). DOI: 10.1214/aos/1176348653


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.


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J. S. Marron. M. P. Wand. "Exact Mean Integrated Squared Error." Ann. Statist. 20 (2) 712 - 736, June, 1992.


Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0746.62040
MathSciNet: MR1165589
Digital Object Identifier: 10.1214/aos/1176348653

Primary: 62G05
Secondary: 65D30

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 2 • June, 1992
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