Open Access
September, 1976 Invariant Quadratic Unbiased Estimation for Two Variance Components
Anthony Olsen, Justus Seely, David Birkes
Ann. Statist. 4(5): 878-890 (September, 1976). DOI: 10.1214/aos/1176343586


For a normally distributed mixed model with two unknown variance components $\theta_1$ and $\theta_2$, a tractable characterization is given for the admissible estimators within the class $\tilde{\mathscr{N}}_\delta$ of invariant quadratic unbiased estimators for $\delta_1\theta_1 + \delta_2\theta_2$. Here the term admissible is used with reference only to the class $\tilde{\mathscr{N}}_\delta$. This characterization is based on a result for general linear models which characterizes the admissible estimators within the class of linear unbiased estimators. The admissibility of MINQUE estimators and the usual analysis of variance estimators is considered.


Download Citation

Anthony Olsen. Justus Seely. David Birkes. "Invariant Quadratic Unbiased Estimation for Two Variance Components." Ann. Statist. 4 (5) 878 - 890, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0344.62060
MathSciNet: MR418345
Digital Object Identifier: 10.1214/aos/1176343586

Primary: 62J99
Secondary: 62C15

Keywords: Admissibility , complete class , Henderson method III , MINQUE , quadratic estimators , variance components

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
Back to Top