Breakdown properties of location M-estimators

• 成果类型: Article
• 署名作者: Zhang, J; Li, GY
• 署名单位: Chinese Academy of Sciences
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1170-1189
• 关键词: finite-sample breakdown; regression; definition; Robustness; points; tests

摘要

In this article, we consider the asymptotic behavior of three kinds of sample breakdown points. It is shown that for the location M-estimator with bounded objective function, both the addition sample breakdown point and the simplified replacement sample breakdown point strongly converge to the gross-error asymptotic breakdown point, whereas the replacement sample breakdown point strongly converges to a smaller value. In addition, it is proved that under some regularity conditions these sample breakdown points are asymptotically normal. The addition sample breakdown point has a smaller asymptotic variance than the simplified replacement sample breakdown point. For the commonly used redescending M-estimators of location, numerical results indicate that among the three kinds of sample breakdown points, the replacement sample breakdown point has the largest asymptotic variance.