Functional stability of one-step GM-estimators in approximately linear regression

• 成果类型: Article
• 署名作者: Simpson, DG; Yohai, VJ
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1024691092
• 发表日期: 1998
• 页码: 1147-1169
• 关键词: unmasking multivariate outliers; high breakdown-point; s-estimators; robust regression; bounded-influence; leverage points; BIAS; asymptotics; location; projections

摘要

This paper provides a comparative sensitivity analysis of one-step Newton-Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by epsilon-contamination of the model. These bounds yield breakdown points and local rates of convergence of the bias as epsilon decreases to zero. We treat a unified class of Newton-Raphson estimators, including one-step versions of the well-known Schweppe, Mallows and Hill-Ryan GM estimators. Of the three well-known types, the Hill-Ryan form emerges as the most stable in terms of one-step estimation. The Schweppe form is susceptible to a breakdown of the Hessian matrix. For this reason it fails to improve on the local stability of the initial estimator, and it may lead to falsely optimistic estimates of precision.