Rate of convergence of depth contours: with application to a multivariate metrically trimmed mean

✍ Scribed by Jeankyung Kim

• Book ID: 104301450
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 102 KB
• Volume: 49
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(00)00073-0

✦ Synopsis

In a recent paper of He and Wang (1997, Ann. Statist. 25, 495-504), they considered depth contours based on data depth and they proved a uniform contour convergence theorem under some conditions on the depth measure. In this paper we prove n -1=2 rate of convergence of depth contours using empirical process and U-process theory. This result is then applied to get n -1=2 rate of convergence of a multivariate metrically trimmed mean.