Breakdown points of trimmed likelihood estimators and related estimators in generalized linear models

Lower bounds for breakdown points of trimmed likelihood (TL) estimators in a general setup are expressed by the fullness parameter of Vandev (Statist. Probab. Lett. 16 (1993) 117) and results of Vandev and Neykov (Statistics 32 (1998) 111) are extended. A special application of the general result is the breakdown point behavior of TL estimators and related estimators as the S estimators in generalized linear models. For the generalized linear models, a connection between the fullness parameter and the quantity N(X) of Muller (J. Statist. Plann. Inference 45 (1995) 413) is derived for the case that the explanatory variables may not be in general position which happens in particular in designed experiments. These results are in particular applied to logistic regression and log-linear models where upper bounds for the breakdown points are also derived. (C) 2002 Elsevier B.V. All rights reserved.