5 Concluding remarks
Yong You, J.N.K. Rao and Mike Hidiroglou
We have studied the properties of the EBLUP and two self-benchmarking estimators, YR and WFQ, under the Fay-Herriot area level model. We presented a nearly unbiased estimator of MSPE of the YR estimator in Section 3. Our simulation results indicate that the three methods perform very similarly with respect to MSPE of the estimators and RB and CV of the MSPE estimators. However, under gross model misspecification due to an omitted variable, MSPE is significantly increased for all the three estimators, unless the augmented model of WFQ nearly eliminates misspecification. In practice, it is difficult to account for model misspecification due to unknown omitted variables. It is also interesting to note that self-benchmarking may not reduce bias under model misspecification that is not accounted by the augmented model of WFQ.
Acknowledgements
We are thankful to a referee and the Associate Editor for many constructive comments and suggestions.
References
Fay, R.E., and Herriot, R.A. (1979). Estimation of income for small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association, 74, 268-277.
Rao, J.N.K. (2003). Small Area Estimation, New York: John Wiley & Sons, Inc.
Wang, J., Fuller, W.A. and Qu, Y. (2008). Small area estimation under a restriction. Survey Methodology, 34, 1, 29-36.
You, Y., and Rao, J.N.K. (2002). A pseudo empirical best linear unbiased prediction approach to small area estimation using survey weights. The Canadian Journal of Statistics, 30, 431-439.
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