Variance Component Estimation in General Mixed Model of Analysis of Variance

For a general mixed model a set of quadratic sufficient statistics is formed assuming initially the fixed effect parameters to be known and the weighted least squares (WLS) technique is then applied on the basis of these statistics. The estimate is finally obtained by replacing the true variances in the weights by some suitable consistent estimates. The fixed effect parameters assumed to be known earlier are also replaced by some consistent estimates. The estimate is generally simpler to calculate than the maximum likelihood estimate (MLE). It is also best asymptotically normal (BAN) in the same sense as the MLE for design sequences whose size increases to infinity in an orderly way. In fact for such design sequences the estimate is asymptotically equivalent to the MLE.