Nonnegative unbiased estimability of linear combinations of two variance components
For a general mixed model with two variance components \(\theta_ 1\) and \(\theta_ 2\), a criterion for a function \(q_ 1\theta_ 1+q_ 2\theta_ 2\) to admit an unbiased nonnegative definite quadratic estimator is established in a form that allows answering the question of existence of such an estimator more explicitly than with the use of the criteria known hitherto. An application of this result to the case of a random one-way model shows that for many unbalanced models the estimability criterion is expressible directly by the largest of the numbers of observations within levels, thus extending the criterion established by \textit{L. R. LaMotte} [J. Am. Stat. Assoc. 68, 728-730 (1973; Zbl 0271.62093)] for balanced models.
unbiased nonnegative definite quadratic estimator
scientific article; zbMATH DE number 3898041