1994 年 15 巻 1 号 p. 1-16
The sampling variances of estimators of variance cnmponents in the basic mixed linear model are derived for an approximate approach to the minimum variance quadratic unbiased estimation. The assumption made with the basic model is that the variance-covariance matrix for the ith random factor has the form Iσ* where I is an identity matrix of order equal to the number of levels for the factor and σ* is the variance component to be estimated. Assuming a two-way crossclassified model including fixed herd and random sire and residual effects in applied animal breeding and considering a certain unbalanced data structure, the efficiencies of estimators of variances of the two random effects by the approximate method, relative to the minimum variance quadratic unbiased estimators which are the best estimators, are numerically investigated within the parameter space of heritability which can be expressed as a function of the ratio of residual variance to sire variance and with choosing its prior values. The sampling variance of the estimator of sire variance with the approximate method is shown to be not minimized by choosing the prior value of heritability to be the true value, as is not the case with the minimum variance quadratic unbiased estimation. For a given data structure, with the approximate method, it is found that using a constant prior value of moderate magnitude for heritability gives the efficiencies of the estimator of sire variance higher than. 8 over the given range of the parameter.