In the variance component model , Pukelsheim proved that the non-negative and unbiased estimation of the variance component entails a transformation of the original model to (called the Q-reduced model). Lee and Kapadia, considered the maximum likelihood approach based on the likelihood of the (denoted by ) and applied to an incomplete block design model. In this note, the results given in their paper are used to show that the variance of the combined estimator of treatment contrast proposed by Graybill and Deal can be reduced if the estimators of the variance components are used instead of AOV estimators as is done in Graybill and Deal's paper.
