Quadratic unbiased estimation without invariance and its application in the unbalanced one-way random model. (English) Zbl 0744.62097
Summary: Quadratic unbiased estimation in a general mixed model is considered. It was recently proved by the author [Ann. Inst. Stat. Math. 39, 563-573 (1987; Zbl 0691.62010)] 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.
Keywords:
variance components; without invariance; Lehmann-Scheffé theorem; general mixed model; locally best quadratic unbiased estimators; locally best invariant quadratic unbiased estimator; explicit formulae; variances; unbalanced one-way random modelCitations:
Zbl 0691.62010References:
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