A Review of Linear Mixed Models and Small Area Estimation
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.
|Date of creation:||Dec 2009|
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- Gauri Sankar Datta, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152.
- Basu, Ruma & Ghosh, J. K. & Mukerjee, Rahul, 2003. "Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 197-203, June.
- Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238.
- Cressie, N. & Lahiri, S. N., 1993. "The Asymptotic Distribution of REML Estimators," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 217-233, May.
- Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
- Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
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