Covariance based moment equations for improved variance component estimation

ANOVA-based estimators of variance components for nested-error regression models are always constructed based on moment equations through residual variance. We consider moment equations associated with residual covariance and construct improved ANOVA-based estimators. The proposed estimators have closed-form analytic expressions, which enables easy computation. Moreover, they are shown to be consistent, asymptotically unbiased, and robust to the choice of distribution of the random effects. These estimators have comparable and often better performances than many traditional estimators of variance components like the Prasad-Rao, maximum likelihood, and the restricted maximum likelihood estimators for almost all kinds of sample allocations. Their improved performances are demonstrated analytically as well as through detailed simulation studies and applications to real data sets.