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June 2010 Asymptotics and optimal bandwidth selection for highest density region estimation
R. J. Samworth, M. P. Wand
Ann. Statist. 38(3): 1767-1792 (June 2010). DOI: 10.1214/09-AOS766

Abstract

We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.

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R. J. Samworth. M. P. Wand. "Asymptotics and optimal bandwidth selection for highest density region estimation." Ann. Statist. 38 (3) 1767 - 1792, June 2010. https://doi.org/10.1214/09-AOS766

Information

Published: June 2010
First available in Project Euclid: 24 March 2010

zbMATH: 1189.62061
MathSciNet: MR2662359
Digital Object Identifier: 10.1214/09-AOS766

Subjects:
Primary: 62G07 , 62G20

Keywords: Density contour , Density level set , kernel density estimator , plug-in bandwidth selection

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 3 • June 2010
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