Fast and robust estimators of variance components in the nested error model

Usual fitting methods for the nested error linear regression model are known to be very sensitive to the effect of even a single outlier. Robust approaches for the unbalanced nested error model with proved robustness and efficiency properties, such as M-estimators, are typically obtained through iterative algorithms. These algorithms are often computationally intensive and require robust estimates of the same parameters to start the algorithms, but so far no robust starting values have been proposed for this model. This paper proposes computationally fast robust estimators for the variance components under an unbalanced nested error model, based on a simple robustification of the fitting-of-constants method or Henderson method III. These estimators can be used as starting values for other iterative methods. Our simulations show that they are highly robust to various types of contamination of different magnitude.