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Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model

Author

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  • Kleffe, J.
  • Rao, J. N. K.

Abstract

A linear model with random effects, [mu]i, and random error variances, [sigma]i, is considered. The linear Bayes estimator or the best linear unbiased predictor (BLUP) of [mu]i is first obtained, and then the unknown parameters in the model are estimated to arrive at the empirical linear Bayes estimator or the empirical BLUP (EBLUP) of [mu]i. A second-order approximation to mean square error (MSE) of the EBLUP and an approximately unbiased estimator of MSE are derived. Results of a simulation study confirm the accuracy of these approximations.

Suggested Citation

  • Kleffe, J. & Rao, J. N. K., 1992. "Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 1-15, October.
    • Handle: RePEc:eee:jmvana:v:43:y:1992:i:1:p:1-15
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    Citations

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    Cited by:

    1. Júlia Volaufová, 1995. "The empirical linear predictor and its MSE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 260-260, December.
    2. Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    3. Peter A. Gao & Jonathan Wakefield, 2023. "A Spatial Variance‐Smoothing Area Level Model for Small Area Estimation of Demographic Rates," International Statistical Review, International Statistical Institute, vol. 91(3), pages 493-510, December.

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