ASPECTS OF ROBUST LINEAR-REGRESSION

• 成果类型: Article
• 署名作者: DAVIES, PL
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349401
• 发表日期: 1993
• 页码: 1843-1899
• 关键词: high breakdown-point; bounded-influence regression; multivariate location; M-ESTIMATORS; frechet differentiability; asymptotic-behavior; squares regression; s-estimators; scale; EFFICIENCY

摘要

Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that S-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of the Krasker-Welsch dispersion functional is obtained as well as bounds for the corresponding regression functional. Section 6 contains the construction of a linearly equivariant, high breakdown and locally Lipschitz dispersion functional for any design distribution. In Section 7 it is shown that there is no inherent contradiction between efficiency and a high breakdown point. Section 8 contains a linearly equivariant, high breakdown regression functional which is Lipschitz continuous at models with normal errors.