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Mean driven balance and uniformly best linear unbiased estimators

Author

Listed:
  • Roman Zmyślony
  • João Mexia
  • Francisco Carvalho
  • Inês Sequeira

Abstract

The equivalence of ordinary least squares estimators (OLSE) and Gauss–Markov estimators for models with variance–covariance matrix $$\sigma ^2{\mathbf M}$$ σ 2 M is extended to derive a necessary and sufficient balance condition for mixed models with mean vector $${\varvec{\mu }}={{\mathbf X} {\varvec{\beta }}}$$ μ = X β , with $${\mathbf {X}}$$ X an incidence matrix, having OLSE for $$\varvec{\beta }$$ β that are best linear unbiased estimator whatever the variance components. This approach leads to least squares like estimators for variance components. To illustrate the range of applications for the balance condition, interesting special models are considered. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Roman Zmyślony & João Mexia & Francisco Carvalho & Inês Sequeira, 2016. "Mean driven balance and uniformly best linear unbiased estimators," Statistical Papers, Springer, vol. 57(1), pages 43-53, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:43-53
    DOI: 10.1007/s00362-014-0638-y
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    References listed on IDEAS

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    1. Butte Gotu, 2001. "The equality of OLS and GLS estimators in the linear regression model when the disturbances are spatially correlated," Statistical Papers, Springer, vol. 42(2), pages 253-263, April.
    2. Oskar Baksalary & Götz Trenkler & Erkki Liski, 2013. "Let us do the twist again," Statistical Papers, Springer, vol. 54(4), pages 1109-1119, November.
    3. Jarkko Isotalo & Simo Puntanen, 2009. "A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model," Statistical Papers, Springer, vol. 50(1), pages 185-193, January.
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