Abstract: This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is large enough to include popular high breakdown point estimators such as S-estimators and MM-estimators, which were not covered by existing results in the literature. We prove consistency assuming only that and asymptotic normality essentially if where p is the number of covariates and n is the sample size.

Key words and phrases: Dimension asymptotics, M-estimators, MM-estimators, robust regression, S-estimators.