Robust Estimation of Variance Components

Outliers may occur with respect to any of the random components in the mixed linear model. A procedure for limiting the influence of these outliers on the estimates of the model parameters is described. Given the variances or estimates of them, the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances. Large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects, as appropriate, and Winsorized. The robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of Huber's proposal 2. A numerical example illustrates the use of the methodology, both as a diagnostic and as an estimation tool.