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Breakdown points of t-type regression estimators. (English) Zbl 1120.62320
Summary: To bound the influence of a leverage point, generalised M-estimators have been suggested. However, the usual generalised M-estimator of regression has a breakdown point that is less than the inverse of its dimension. This paper shows that dimension-independent positive breakdown points can be attained by a class of well-defined generalised M-estimators with redescending scores. The solution can be determined through optimisation of t-type likelihood applied to properly weighted residuals. The highest breakdown point of 1 2; is attained by Cauchy score. These bounded-influence and high-breakdown estimators can be viewed as a fully iterated version of the one-step generalised M-estimates of Simpson, Ruppert and Carroll (1992) with the two advantages of easier interpretability and avoidance of undesirable roots to estimating equations. Given the design-dependent weights, they can be computed via EM algorithms. Empirical investigations show that they are highly competitive with other robust estimators of regression.
MSC:
62J05Linear regression
62F35Robustness and adaptive procedures (parametric inference)
62F10Point estimation