Best estimation of variance components from balanced data, with arbitrary kurtosis

Properties are well known for analysis of variance estimators of variance components obtained from balanced data under assumptions either of normality or of zero kurtosis. We show here that even with non-zero kurtosis, these estimators still have uniformly minimum variance among all unbiased, translation invariant, quadratic estimators Example of balnced data models with succinet matrix representations are given An algorithem pred\sends for derving from xx the matrix m=i-xx where x is the ncidence matrix for the fixed effeets and x +denotes its Moore Penrse inverse. The algoritham involves only the kronecker prodct operation and require no explicit calculation of generalized incveescs.