Abstract
The paper considers stochastic convergence of certain means used to obtain the between sum of squares in analysis of variance. These limiting random variables are used to obtain a nonnegative estimator of the between component of variance. The usual ANOVA estimator of the within component of variance is considered. A nonnegative estimator of heritability is given. Asymptotic tests are derived also. Finally, the paper extends the linear model to allow the number of observations in each cell to be random.
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