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Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

The 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.

Suggested Citation

  • Tatsuya Kubokawa, 2012. "Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation," CIRJE F-Series CIRJE-F-832, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2012cf832
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    References listed on IDEAS

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    1. 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.
    2. 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;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    3. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
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    Cited by:

    1. Tatsuya Kubokawa & Mana Hasukawa & Kunihiko Takahashi, 2014. "On Measuring Uncertainty of Benchmarked Predictors with Application to Disease Risk Estimate," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 394-413, June.
    2. Tatsuya Kubokawa & Mana Hasukawa & Kunihiko Takahashi, 2012. "On Measuring Uncertainty of Benchmarked Predictors with Application to Disease Risk Estimatee," CIRJE F-Series CIRJE-F-861, CIRJE, Faculty of Economics, University of Tokyo.

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