On the maximum bias functions of MM-estimates and constrained M-estimates of regression

• 成果类型: Article
• 署名作者: Berrendero, Jose R.; Mendes, Beatriz V. M.; Tyler, David E.
• 署名单位: Autonomous University of Madrid; Universidade Federal do Rio de Janeiro; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000975
• 发表日期: 2007
• 页码: 13-40
• 关键词: high breakdown-point; robust regression; PROPERTY; Minimax

摘要

We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the tau-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is, the resulting CM-estimate dominates the S-estimate in terms of maxbias and, at the same time, is considerably more efficient.