Measuring uncertainty associated with model-based small area estimators
Section 6. Conclusions
In this paper we studied the properties of alternative MSE estimators in tracking the design MSE of EB estimators of small area means. We examined both area level and unit level models.
In the area level model, we proposed two composite MSE estimators by taking a weighted average of a design unbiased MSE estimator and a model based MSE estimator. Modifications to ensure positive MSE estimators were also given. Performance of the alternative MSE estimators was studied through simulations in terms of absolute relative bias, relative root mean square error and coverage rate of confidence intervals. Our results for the area level model suggest that the design unbiased MSE estimator is not usable in practice when the area sample size is very small because of a large probability of getting a negative value. On the other hand, this probability for the composite 1 MSE estimator (with the same weights as the EB estimator), is either zero or essentially negligible. Our simulations for the area level model for areas with very small sample sizes suggest that the composite 1 MSE estimator leads to smaller ARB relative to the model MSE estimator at the expense of an increase in RRMSE. For areas with larger sample sizes, the ARB of the model MSE estimator persists unlike the ARB of the composite 1 MSE estimator. In terms of coverage rates, the model MSE estimator and the composite 1 MSE estimator are comparable across all areas, but both can lead to serious undercoverage for areas with very small sample sizes. Overall, the composite 1 MSE estimator provides a good compromise in estimating the design MSE.
In the simulation study of the unit level model, our results suggest that the composite MSE estimator generally offers a good compromise between the ARB and RRMSE. However, the plug-in design MSE estimator used in the composite estimator needs modification to take account of the variability in the estimators of model parameters to avoid or reduce the underestimation of design MSE of the EB estimator.
Acknowledgements
The authors thank the assistant and associate editors and the two referees for their comments and suggestions that led to improvements in our examination of the various MSE estimators.
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