Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation
AbstractThe empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation in the sense of increasing the precision of estimation of small area means. However, one potential difficulty of EBLUP is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate like the overall sample mean. One way to solve this problem is the benchmarking approach, and the constrained EBLUP is a feasible solution which satisfies the constraints that the aggregated mean and variance are identical to the requested values of mean and variance. An interesting query is whether the constrained EBLUP may have a larger estimation error than EBLUP. In this paper, we address this issue by deriving asymptotic approximations of MSE of the constrained EBLUP. Also, we provide asymptotic unbiased estimators of the MSE of the constrained EBLUP based on the parametric bootstrap method, and establish their second-order justification. Finally, the performances of the suggested MSE estimators are numerically investigated.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-832.
Length: 21 pages
Date of creation: Jan 2012
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- G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(3), pages 574-588, November.
- 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.
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