A Comparison of Variances of Some Estimators in the Balanced Incomplete Block (BIB) Variance Components Model

A way is described of obtaining the variances of Henderson's [1953] Methods 1 and 3 estimates in a BIB with random effects, when normality is assumed. We illustrate the method by an example, showing that an estimator indicated by the minimal sufficient but not complete set of statistics given by Weeks and Graybill [1961] has variance which can exceed that of another estimator, and so is not MV. We give tentative conclusions regarding the choice of estimator in practice.