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September, 1985 An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation
James Stephen Marron
Ann. Statist. 13(3): 1011-1023 (September, 1985). DOI: 10.1214/aos/1176349653

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.

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James Stephen Marron. "An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation." Ann. Statist. 13 (3) 1011 - 1023, September, 1985. https://doi.org/10.1214/aos/1176349653

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0585.62073
MathSciNet: MR803755
Digital Object Identifier: 10.1214/aos/1176349653

Subjects:
Primary: 62G05
Secondary: 62G20

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September, 1985
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