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ONE-STEP-M-ESTIMATORS IN CONDITIONALLY CONTAMINATED LINEAR MODELS

The notion of one-step-M-estimators is generalized for estimating general linear aspects of homoscedastic or heteroscedastic conditionally contaminated linear models with general parametrization and general underlying design. For such contaminated lineal: models it is shown that the generalized one-step-M-estimators at random and deterministic designs with finite support are asymptotically normally distributed with maximum asymptotic bias and asymptotic covariance matrix only depending on the score function of the one-step-M-estimator and the true variances of the model. This is obtained by deriving their asymptotic linearity under relative simple assumptions which are easy to verify and which admit a wide scope of applications. An example demonstrates the applicability of the results.