Abstract
Quadratic unbiased estimation in a general mixed model is considered. It was recently proved in Stępniak (1987, Ann. Inst. Statist. Math. 39, 563–573) that any admissible estimator in the problem is a limit of unique locally best quadratics in a wide sense. We focus on the usual locally best quadratic unbiased estimators (LBQUE's). It is shown, that any locally best invariant quadratic unbiased estimator (or MINQUE with invariance) is a limit of LBQUE's. Explicit formulae for LBQUE's and their variances are given. The unbalanced one-way random model is considered in detail.
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