Pseudo Expectation Approach to Variance Component Estimation

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Abstract
Quadratic forms utilizing solutions to best linear unbiased prediction equations after absorbing all fixed effects into the equations for random effects were computed and pseudo expectations derived. Pseudo expectations are taken as if a priori values are equal to true values rather than being taken as constants. Quadratic forms different from restricted maximum likelihood forms yielded estimators that did not depend on the inverse of mixed model equations, and estimators were always positive. This approach offers computational advantages over most other methods. Theoretically, this method has properties similar to restricted maximum likelihood. Application to models involving additive genetic relationships and models with covariances among levels of two random factors were outlined.