On measuring the variability of small area estimators under a basic area level model
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Biometrika Trust in its journal Biometrika.
Volume (Year): 92 (2005)
Issue (Month): 1 (March)
Contact details of provider:
Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
Fax: 01865 267 985
Web page: http://biomet.oxfordjournals.org/
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- Ganesh, N., 2009. "Simultaneous credible intervals for small area estimation problems," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1610-1621, September.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.