Best estimation of variance components with arbitrary kurtosis in two-way layouts mixed models

Abstract

Under the assumptions that a linear model corresponding to two-way layouts is the mixed model without interaction, necessary and sufficient conditions are derived under which the minimum norm invariant quadratic unbiased estimators have uniformly minimum variance among all unbiased invariant quadratic estimators for data with arbitrary kurtosis. The conditions are expressed in terms of the incidence matrix N and C-matrix of the design. Under the model considered in this paper, the results obtained here strengthen those by Anderson et al. (1984), where data are required to satisfy a special balance condition.