M-Methods in multivariate linear models

For the multivariate linear model, coordinatewise M-estimators as well as an extension of the Maronna-type M-estimators are considered. Based on the Jurecková (asymptotic) linearity of M-statistics, the asymptotic distribution theory of the proposed estimators is studied under appropriate regularity conditions, and incorporated in the formulation of some (asymptotic) M-tests of linear hypotheses. Finally, robustness properties of both types of estimators are discussed.