Improving Henderson's Method 3 Approach when Estimating Variance Components in a Two-way Mixed Linear Model


A two-way linear mixed model, consisting of three variance components, σ1 2, σ2 2 and σe 2 is considered. The variance component estimators are estimated using a well known non-iterative estimation procedure, Henderson's method 3. for σ2 1 we propose two modified estimators. The modification is carried out by perturbing the standard estimator, such that the obtained estimator is expected to perform better in terms of its mean square error.


Mean Square Error Variance Component Unbiased Estimator Estimate Variance Component Unbalanced Data 
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  1. 1.
    Graybill, F.A., Hultquist, R.A.: Theorems concerning Eisenhart's Model II. Ann. Math. Stat. 32, 261–269 (1961)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Henderson, C.R.: Estimation of variance and covariance components. Biometrics 9, 226–252 (1953)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Kelly, J.R., Mathew, T.: Improved nonnegative estimation of variance components in some mixed models with unbalanced data. Technometrics 36, 171–181 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    LaMotte, L.R.: On non-negative quadratic unbiased estimation of variance components. J. Am. Stat. Assoc. 68, 728–730 (1973)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Schott, J.R.: Matrix analysis for statistics. Wiley, New York (1997)MATHGoogle Scholar
  6. 6.
    Searle, S.R.: Another look at Henderson's methods of estimating variance components. Biometrics 24, 749–778 (1968)CrossRefGoogle Scholar
  7. 7.
    Searle, S.R.: Linear models. Wiley, New York (1971)MATHGoogle Scholar
  8. 8.
    Searle, S.R.: Linear models for unbalanced data. Wiley, New York (1987)Google Scholar
  9. 9.
    Searle, S.R., Casella, G., McCulloch, C.E.: Variance components. Wiley, New York (1992)MATHGoogle Scholar

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© Physica-Verlag Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Energy and TechnologyUppsalaSweden

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