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

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  • Mathew, Thomas
  • Sinha, Bimal Kumar
  • Sutradhar, Brajendra C.

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.

Suggested Citation

  • Mathew, Thomas & Sinha, Bimal Kumar & Sutradhar, Brajendra C., 1992. "Nonnegative estimation of variance components in unbalanced mixed models with two variance components," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 77-101, July.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:77-101
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    Cited by:

    1. Bobotas, Panayiotis & Kourouklis, Stavros, 2017. "Estimation of the smallest normal variance with applications to variance components models," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 38-45.
    2. Sutradhar, Brajendra C., 1997. "A multivariate approach for estimating the random effects variance component in one-way random effects model," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 333-339, May.
    3. Molinska, Anna & Molinski, Krzysztof, 1995. "Improvement of ANOVA estimators of variance components in block designs with random treatments," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 281-285, March.

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