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arXiv · 1010.0591

Asymptotics and optimal bandwidth selection for highest density region estimation

R. J. Samworth·M. P. Wand
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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. 2010-10-04. Asymptotics and optimal bandwidth selection for highest density region estimation. https://doi.org/10.1214/09-aos766

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