Asymptotics and optimal bandwidth selection for highest density region estimation

Details Asymptotics and optimal bandwidth selection for highest density region estimation Asymptotics and optimal bandwidth selection for highest density region estimation

2010-10-04

arxiv.org/abs/1010.0591v1

Annals of Statistics 2010, Vol. 38, No. 3, 1767-1792

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS766 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS766

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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