Asymptotics and Optimal Bandwidth Selection for Highest Density Region Estimation

Authors

R. J. Samworth, University of Cambridge
M. P. Wand, University of WollongongFollow

Publication Date

2009

Recommended Citation

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.
https://ro.uow.edu.au/cssmwp/22

Abstract

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.