Nonnegative estimation of variance components in unbalanced mixed models with two variance components

Thomas Mathew, Bimal Kumar Sinha and Brajendra C. Sutradhar

Journal of Multivariate Analysis, 1992, vol. 42, issue 1, 77-101

Abstract: An unbalanced mixed linear model with two variance components is considered, one variance component (say [sigma]12 >= 0) corresponding to a random effect (treatments) and a second variance component (say [sigma]2 > 0) corresponding to the experimental errors. Sufficient conditions are obtained under which there will exist a nonnegative invariant quadratic estimator (IQE) having a uniformly smaller mean squared error (MSE) than every unbiased IQE of [sigma]12. In particular, for the one-way unbalanced ANOVA model, necessary and sufficient conditions are also obtained for a multiple of the usual treatment sum of squares to uniformly dominate the ANOVA estimator of [sigma]12. For estimating [sigma]2, it is shown that the best multiple of the residual sum of squares can be improved by using nonquadratic estimators. One such estimator is obtained using the idea of a testimator ([13], Ann. Inst. Statist. Math.16 155-160). A second estimator is obtained following the approach in [14], Ann. Statist.2 190-198). Numerical results regarding the performance of the proposed estimators of [sigma]12 are also reported.

Keywords: invariant; quadratic; estimator; MINQUE; nonquadratic; estimator; one-way; classification; testimator; unbalanced; models (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (3)

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