The Annals of Statistics

Asymptotics and optimal bandwidth selection for highest density region estimation

R. J. Samworth and M. P. Wand

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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.

Article information

Ann. Statist., Volume 38, Number 3 (2010), 1767-1792.

First available in Project Euclid: 24 March 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G20: Asymptotic properties

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


Samworth, R. J.; Wand, M. P. Asymptotics and optimal bandwidth selection for highest density region estimation. Ann. Statist. 38 (2010), no. 3, 1767--1792. doi:10.1214/09-AOS766.

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