Samworth, R. J. and Wand, M. P., Asymptotics and Optimal Bandwidth Selection for Highest Density Region Estimation, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 02-09, 2009, 23p.
We study kernel estimation of highest density regions (HDR). Our main contributions are twofold. Firstly, 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.