ASYMPTOTICS AND OPTIMAL BANDWIDTH SELECTION FOR HIGHEST DENSITY REGION ESTIMATION

• 成果类型: Article
• 署名作者: Samworth, R. J.; Wand, M. P.
• 署名单位: University of Cambridge; University of Cambridge; University of Wollongong
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS766
• 发表日期: 2010
• 页码: 1767-1792
• 关键词: nonparametric-estimation; rates; contour

摘要

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.