Maximum bias curves for robust regression with non-elliptical regressors

• 成果类型: Article
• 署名作者: Berrendero, JR; Zamar, RH
• 署名单位: Autonomous University of Madrid; University of British Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/996986507
• 发表日期: 2001
• 页码: 224-251
• 关键词: high breakdown-point; linear-regression; s-estimators; scale; STABILITY; Minimax; contamination

摘要

Maximum bias curves for some regression estimates were previously derived assuming that (i) the intercept term is known and/or (ii) the regressors have an elliptical distribution. We present a single method to obtain the maximum bias curves for a large class of regression estimates. Our results are derived under very mild conditions and, in particular, do not require the restrictive assumptions (i) and (ii) above. Using these results it is shown that the maximum bias curves heavily depend on the shape of the regressors' distribution which we call the x-configuration. Despite this big effect, the relative performance of different estimates remains unchanged under different x-configurations. We also explore the links between maxbias curves acid bias bounds. Finally, we compare the robustness properties of some estimates for the intercept parameter.