4 Best Quadratic Unoiased Estimation of Variance CoMponents from

N.Y. Best quadrati.c unbiased estimators (BQUE ' s) of variance components from unbalanced data in the one-way classification random model are derived under zero mean and normality as~ptions. An estima~r or the between-class variance is also developed for the non-zero mean case fron analogy with the zero mean situation. These estirnators a.re fullctions of tbe ratio of the population variances, p = a!(a ~. Nwnerical studies indicate that for,badly unbalanced data and for values of p larger than one, estimators of • 2 having a variance less than that or the analysis of variance estimator can be obtained by substituting even a rather inaccurately predetermined value of p into the BQUE of a2