Abstract
A set of quadratic forms are proposed, which contain an approximate solution vector and the right-hand side vector in the mixed model equations after absorption of fixed effects on one and another side, respectively. The approximate solutions are based on utilizing information included in the offdiagonal elements as well as in the diagonal elements of the coefficient matrix. The quadratics are translation invariant and whose matrices are not symmetric. Using the quadratics, a method for unbiased estimation of variance components in the mixed linear model is described as a simple approximation to the minimum variance quadratic unbiased estimation. The current approach does not require the calculation of a generalized inverse of the coefficient matrix as do not other approximate approaches. The relative ability of the present method to eliminate bias due to a culling tyqe of selection is examined by Monte Cario simulation.
