A General Approach to the Estimation of Variance Components

A general method of estimation of variance components in random-effects models of the nested and/or classification type is considered. If a given parameter is estimable with respect to some particular experimental design (i. e., an unbiased estimate of the parameter may be obtained from the experiment), then the suggested estimator may be readily computed with only the aid of a desk calculator. The estimates are always unbiased and consistent (with respect to the structure of the experimental design); in the case of balanced experiments, they coincide with those obtained from the analysis of variance. Secondly, the problem of designing experiments to estimate variance components is briefly discussed from the point-of-view of the suggested estimation procedure. As a result, certain non-balanced designs are seen to yield more efficient estimators of particular parameters in specified situations than the corresponding balanced design using the same number of observations. Finally, the method of estimation is shown to be applicable to models more general than the variance component one. Again it is readily computed and is unbiased and consistent.