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Minimum variance quadratic unbiased estimation of variance components

Author

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  • Rao, C. Radhakrishna

Abstract

The variance of a quadratic function of the random variables in a linear model is minimized to obtain locally best unbiased estimators (MIVQUE) of variance components. Condition for such estimators to be independent of the kurtosis of the variables is given. When the variables are normally distributed, MIVQUE coincides with MINQUE under the Euclidean norm of a matrix. Conditions under which MIVQUE has uniformly minimum variance property are obtained. Expressions are also given for MIMSQE (minimum mean square quadratic estimators).

Suggested Citation

  • Rao, C. Radhakrishna, 1971. "Minimum variance quadratic unbiased estimation of variance components," Journal of Multivariate Analysis, Elsevier, vol. 1(4), pages 445-456, December.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:4:p:445-456
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    Cited by:

    1. Jonathan McCarthy & Egon Zakrajšek, 2000. "Microeconomic inventory adjustment: evidence from U.S. firm-level data," Staff Reports 101, Federal Reserve Bank of New York.
    2. Mathias Lindholm & Felix Wahl, 2020. "On the variance parameter estimator in general linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 243-254, February.
    3. S. Cheng & B. Chen, 1991. "The locally MIMSQE of nonnormal error variance in quadratically balanced models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 67-70, December.
    4. Tsai, Ming-Tien, 2004. "Maximum likelihood estimation of covariance matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 292-303, May.
    5. H. Baltagi, Badi & Heun Song, Seuck & Cheol Jung, Byoung, 2001. "The unbalanced nested error component regression model," Journal of Econometrics, Elsevier, vol. 101(2), pages 357-381, April.
    6. D. Rasch & O. Mašata, 2006. "Methods of variance component estimation," Czech Journal of Animal Science, Czech Academy of Agricultural Sciences, vol. 51(6), pages 227-235.
    7. Gelein, Brigitte & Haziza, David & Causeur, David, 2014. "Preserving relationships between variables with MIVQUE based imputation for missing survey data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 197-208.

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