MINQUE Method

The MINQUE method requires a set of a priori values for the variance components or the ratios of the components to the residual variance. The estimators are then functions of the data and of the prior values. When the prior values are proportional to the true but unknown values of each variance component (or ratios of each component to the residual variance), the estimates achieve minimum variance in the class of all unbiased, translation invariant quadratic estimators. Since the variance components are unknown, the correct prior values are seldom found. Therefore, the estimators are unlikely to possess the above optimal properties in reality. Despite this fact, the MINQUE method is popular because of its considerable flexibility with respect to the form of models that can be fitted.

The Variance Components procedure offers two schemes of prior values. The first scheme, MINQUE(0), assigns zero prior values to ratios of variance components to the residual variance. The second scheme, MINQUE(1), gives the ratios unit prior values. With either scheme, a system of linear equations is established based on the prior values and the data. The variables are the ratios of the variance components to the residual variance, and the residual variance itself. The system of linear equations is then solved to obtain the MINQUE estimates.

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