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Estimation of mean squared error of model-based estimators of small area means under a nested error linear regression model

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  • Torabi, Mahmoud
  • Rao, J.N.K.

Abstract

Most of the research on small area estimation has focused on unconditional mean squared error (MSE) estimation under an assumed small area model. Datta et al. (2011) [3] studied conditional MSE estimation of a small area mean under a basic area-level model, conditional on the area-specific direct estimator. In this paper, estimation of a small area mean under a nested error linear regression model is studied, using an empirical best (or Bayes) estimator or a weighted estimator with fixed weights. We derive second-order approximations to unconditional MSE and conditional MSE given the area-specific data and obtain associated second-order correct MSE estimators. The performance of MSE estimators is studied using a simulation experiment as well as a real dataset.

Suggested Citation

  • Torabi, Mahmoud & Rao, J.N.K., 2013. "Estimation of mean squared error of model-based estimators of small area means under a nested error linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 76-87.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:76-87
    DOI: 10.1016/j.jmva.2013.02.008
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    References listed on IDEAS

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    1. Gauri Datta & Tatsuya Kubokawa & Isabel Molina & J. Rao, 2011. "Estimation of mean squared error of model-based small area estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 367-388, August.
    2. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
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    Cited by:

    1. Guo Rui & Zhong Zhaowei, 2017. "Forecasting the Air Passenger Volume in Singapore: An Evaluation of TimeSeries Models," International Journal of Technology and Engineering Studies, PROF.IR.DR.Mohid Jailani Mohd Nor, vol. 3(3), pages 117-123.
    2. Rong Zhu & Guohua Zou & Hua Liang & Lixing Zhu, 2016. "Penalized Weighted Least Squares to Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 736-756, September.
    3. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "On Conditional Mean Squared Errors of Empirical Bayes Estimators in Mixed Models with Application to Small Area Estimation," CIRJE F-Series CIRJE-F-934, CIRJE, Faculty of Economics, University of Tokyo.
    4. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2016. "On conditional prediction errors in mixed models with application to small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 18-33.

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