A Simple 'Synthesis'-Based Method of Variance Component Estimation

Abstract

This paper develops a new algorithm for the estimation of components of variance in the mixed ANOVA model. This algorithm is 'efficient' since the computational effort (measured by the number of products) is proportional to n, the number of observations. The method of estimation on which the algorithm is based can be identified with special cases of both MINQUE (for V = I) and with the first iterate for the solution of the restricted maximum likelihood (REML) equations. Other optimality properties are established, and simple conditions for estimability of the variance components are derived. The consistency of the estimators is proved, and they are therefore effective starting points for a single cycle of maximum likelihood (ML) iterations leading to fully efficient estimates.