ASYMPTOTICS FOR REDESCENDING M-ESTIMATORS IN LINEAR MODELS WITH INCREASING DIMENSION

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 p/n -> 0 and asymptotic normality essentially if p(3)/n -> 0, where p is the number of covariates and n is the sample size.