Minimum variance quadratic unbiased estimation of variance components

The variance of a quadratic function of the random variables in a linear model is minimized to obtain locally best unbiased estimators (MIVQUE) of variance components. Condition for such estimators to be independent of the kurtosis of the variables is given. When the variables are normally distributed, MIVQUE coincides with MINQUE under the Euclidean norm of a matrix. Conditions under which MIVQUE has uniformly minimum variance property are obtained. Expressions are also given for MIMSQE (minimum mean square quadratic estimators).