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.
"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