Asymptotics and Optimal Bandwidth Selection for Highest Density Region Estimation

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Executive Summary

A Highest-Density Region (HDR) for a measurement of interest is a region where the underlying density function exceeds some nominal threshold. Given a random sample from that density, HDR estimation typically involves determination of regions where an estimated density is high. The authors study kernel estimation of Highest-Density Regions (HDR). Their main contributions are two-fold. First, they 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. They also present the results of numerical studies that illustrate the benefits of their theory and methodology.

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