Breakdown points and variation exponents of robust M-estimators in linear models

• 成果类型: Article
• 署名作者: Mizera, I; Müller, CH
• 署名单位: Comenius University Bratislava; University of Gottingen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1164-1177
• 关键词: tail-behavior; unimodality; regression

摘要

The breakdown point behavior of M-estimators in linear models with fixed designs, arising from planned experiments or qualitative factors, is characterized. Particularly, this behavior at fixed designs is quite different from that at designs which can be corrupted by outliers, the situation prevailing in the literature. For fixed designs, the breakdown points of robust M-estimators (those with bounded derivative of the score function), depend on the design and the variation exponent (index) of the scole function This general result implies that the highest breakdown point within all regression equivariant estimators can be attained also by certain M-estimators: those with slowly varying score function, like the Cauchy or slash maximum likelihood estimator. The M-estimators with variation exponent greater than 0, like the L-1 or Huber estimator, exhibit a considerably worse breakdown point behavior.