Robustness of an S-Estimator in the One-Way Random Effects Model

An S-estimator is defined for the one-way random effects model, analogous to an S-estimator in the model of i.i.d. random vectors. The estimator resembles the multivariate S-estimator with respect to existence and weak continuity. The proof of existence of the estimator yields in addition an upper bound for the breakdown point of the S-estimator of one of the variance components which is rather low. An improvement of the estimator is proposed which overcomes this deficiency. Nevertheless this estimator is an example that new problems of robustness arise in more structured models.