Asymptotics and optimal bandwidth selection for highest density region estimation

Institute of Mathematical Statistics
Publication Type:
Journal Article
Annals of Statistics, 2010, 38 (3), pp. 1767 - 1792
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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.
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