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A Review of Linear Mixed Models and Small Area Estimation

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

The linear mixed models (LMM) and the empirical best linear unbiased predictor (EBLUP) induced from LMM have been well studied and extensively used for a long time in many applications. Of these, EBLUP in small area estimation has been recognized as a useful tool in various practical statistics. In this paper, we give a review on LMM and EBLUP from a aspect of small area estimation. Especially, we explain why EBLUP is likely to be reliable. The reason is that EBLUP possesses the shrinkage function and the pooling effects as desirable properties, which arise from the setup of random effects and common paramers in LMM. Such important properties of EBLUP are clarified as well as some recent results of the mean squared error estimation, the confidence interval and the variable selection procedures are summarized.

Suggested Citation

  • Tatsuya Kubokawa, 2009. "A Review of Linear Mixed Models and Small Area Estimation," CIRJE F-Series CIRJE-F-702, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf702
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    References listed on IDEAS

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    8. Tatsuya Kubokawa & Muni S. Srivastava, 2009. "Consistency of the Empirical Bayes Information Criterion for Selecting Variables in Linear Mixed Models," CIRJE F-Series CIRJE-F-614, CIRJE, Faculty of Economics, University of Tokyo.
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