Non-iterative robust estimators of variance components in within-subject designs

Classic estimators of variance components break down in the presence of outliers and perform less efficiently under non-normality. In this article I present simple non-iterative estimators of variance components that are resistant to outliers and robust to systematic departures from normality, such as heavy tailedness of the distribution of responses. The proposed estimators are based on a robust extension of Hocking's AVE approach and are thus called RAVE estimators. I present results from a Monte Carlo comparison of RAVE versus classic estimation methods including maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE). Under simulated deviations from normality, RAVE estimators are associated with smaller mean squared errors than all the comparators, and in the normal case they exhibit a minimal loss in relative efficiency. A numerical example illustrates the proposed methodology.