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We provide a unified approach to a method of estimation of the regressionparameter in balanced linear models with a structured covariance matrix thatcombines a high breakdown point and bounded influence with high asymptoticefficiency at models with multivariate normal errors. Of main interest arelinear mixed effects models, but our approach also includes several otherstandard multivariate models, such as multiple regression, multivariateregression, and multivariate location and scatter. We provide sufficientconditions for the existence of the estimators and corresponding functionals,establish asymptotic properties such as consistency and asymptotic normality,and derive their robustness properties in terms of breakdown point andinfluence function. All the results are obtained for general identifiablecovariance structures and are established under mild conditions on thedistribution of the observations, which goes far beyond models withelliptically contoured densities. Some of our results are new and others aremore general than existing ones in the literature. In this way this manuscriptcompletes and improves results on high breakdown estimation with highefficiency in a wide variety of multivariate models.

Highly Efficient Estimators with High Breakdown Point for Linear Models with Structured Covariance Matrices