Asymptotic distributions of the maximal depth estimators for regression and multivariate location

• 成果类型: Article
• 署名作者: Bai, ZD; He, XM
• 署名单位: National University of Singapore; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1616-1637
• 关键词: breakdown points

摘要

We derive the asymptotic distribution of the maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max-min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey's deepest point based on half-space depth. Results for the special case of two-dimensional problems have been available, but the earlier arguments have relied on some special geometric properties in the low-dimensional space. This paper completes the extension to higher dimensions for both regression and multivariate location models.