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# Best Quadratic Unbiased Estimation of Variance Components from Unbalanced Data in the 1-Way Classification

E. C. Townsend and S. R. Searle
Biometrics
Vol. 27, No. 3 (Sep., 1971), pp. 643-657
DOI: 10.2307/2528602
Stable URL: http://www.jstor.org/stable/2528602
Page Count: 15
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## Abstract

Best quadratic unbiased estimators (BQUE's) of variance components from unbalanced data in the 1-way classification random model are derived under zero mean and normality assumptions. An estimator of the between-class variance is also suggested for the non-zero mean case. These estimators are functions of the ratio of the population variances, $\rho$ = $\sigma^2_a/\sigma^2_e$. Numerical studies indicate that for badly unbalanced data and for values of $\rho$ larger than 1 estimators of $\sigma^2_a$ having variance less than that of the analysis of variance estimator can be obtained by substituting even a rather inaccurately predetermined value of $\rho$ into the BQUE of $\sigma^2_a$.

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