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On measuring the variability of small area estimators under a basic area level model

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  • Gauri Sankar Datta
  • J. N. K. Rao
  • David Daniel Smith
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    Abstract

    In this paper based on a basic area level model we obtain second-order accurate approximations to the mean squared error of model-based small area estimators, using the Fay & Herriot (1979) iterative method of estimating the model variance based on weighted residual sum of squares. We also obtain mean squared error estimators unbiased to second order. Based on simulations, we compare the finite-sample performance of our mean squared error estimators with those based on method-of-moments, maximum likelihood and residual maximum likelihood estimators of the model variance. Our results suggest that the Fay--Herriot method performs better, in terms of relative bias of mean squared error estimators, than the other methods across different combinations of number of areas, pattern of sampling variances and distribution of small area effects. We also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second-order unbiased for the mean squared error. The posterior variance based on such a prior possesses both Bayesian and frequentist interpretations. Copyright 2005, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.183
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 92 (2005)
    Issue (Month): 1 (March)
    Pages: 183-196

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    Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:183-196

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    Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
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    Cited by:
    1. Yoshimori, Masayo & Lahiri, Partha, 2014. "A new adjusted maximum likelihood method for the Fay–Herriot small area model," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 281-294.
    2. Malay Ghosh & Tatsuya Kubokawa & Yuki Kawakubo, 2014. "Benchmarked Empirical Bayes Methods in Multiplicative Area-level Models with Risk Evaluation," CIRJE F-Series CIRJE-F-918, CIRJE, Faculty of Economics, University of Tokyo.
    3. Kubokawa, Tatsuya, 2013. "Constrained empirical Bayes estimator and its uncertainty in normal linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 377-392.
    4. 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.
    5. Tatsuya Kubokawa, 2009. "Corrected Empirical Bayes Confidence Intervals in Nested Error Regression Models," CIRJE F-Series CIRJE-F-632, CIRJE, Faculty of Economics, University of Tokyo.
    6. 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.
    7. 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, vol. 20(2), pages 367-388, August.
    8. Ralf Münnich & Jan Burgard & Martin Vogt, 2013. "Small Area-Statistik: Methoden und Anwendungen," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer, vol. 6(3), pages 149-191, March.
    9. Kojima, Masahiro & Kubokawa, Tatsuya, 2013. "Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 162-174.
    10. Jiming Jiang & En-Tzu Tang, 2011. "The best EBLUP in the Fay–Herriot model," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(6), pages 1123-1140, December.
    11. 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, vol. 15(1), pages 1-96, June.
    12. Ganesh, N., 2009. "Simultaneous credible intervals for small area estimation problems," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1610-1621, September.
    13. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Estimation and Prediction Intervals in Transformed Linear Mixed Models," CIRJE F-Series CIRJE-F-929, CIRJE, Faculty of Economics, University of Tokyo.
    14. Shonosuke Sugasawa & Tatsuya Kubokawa, 2013. " Parametric Transformed Fay-Herriot Model for Small Area Estimation ," CIRJE F-Series CIRJE-F-911, CIRJE, Faculty of Economics, University of Tokyo.
    15. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
    16. 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.
    17. Harm Jan Boonstra & Jan A. Van Den Brakel & Bart Buelens & Sabine Krieg & Marc Smeets, 2008. "Towards small area estimation at Statistics Netherlands," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 21-49.
    18. Tatsuya Kubokawa & William E. Strawderman, 2011. "Admissibility and Minimaxity of Benchmarked Shrinkage Estimators," CIRJE F-Series CIRJE-F-809, CIRJE, Faculty of Economics, University of Tokyo.
    19. Tatsuya Kubokawa & Bui Nagashima, 2011. "Parametric Bootstrap Methods for Bias Correction in Linear Mixed Models," CIRJE F-Series CIRJE-F-801, CIRJE, Faculty of Economics, University of Tokyo.
    20. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    21. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.

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