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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.
62J05Linear regression
62F35Robustness and adaptive procedures (parametric inference)
62F10Point estimation