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Abstract Details

Activity Number: 162
Type: Topic Contributed
Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Survey Research Methods
Abstract - #304208
Title: On Estimation of Mean Squared Errors of Benchmarked Empirical Bayes Estimators
Author(s): Rebecca C Steorts*+ and Malay Ghosh
Companies: Carnegie Mellon University and University of Florida
Address: 6323 Howe Street, Apt. D, Pittsburgh, PA, 15206,
Keywords: Fay-Herriot ; benchmarking ; EBLUP ; area-level ; bootstrap ; MSE
Abstract:

Due to the fact that they borrow strength, model-based estimates typically show a substantial improvement over direct estimates in terms of mean squared error (MSE). It is of particular interest to determine how much of this advantage is lost by constraining the estimates through benchmarking. In our paper, we show that the increase due to benchmarking is $O(m^{-1})$, where m is the number of small areas.

In this work, we are concerned with the basic area-level model of Fay and Herriot (1979). We obtain benchmarked empirical Bayes (EB) estimators, and then we derive a second-order asymptotic expansion of the MSE of the benchmarked empirical Bayes estimator. Furthermore, we find an estimator of this MSE and compare it the to second-order approximation of the mean squared error of the empirical best linear unbiased predictor (EBLUP), which was derived by Prasad and Rao (1990). We then compare the estimate of our MSE approximation to the estimate of MSE of the EBLUP in Prasad and Rao (1990). Finally, using methods similar to that of Butar and Lahiri (2003), we compute a parametric double bootstrap estimate of the mean squared error of the benchmarked empirical Bayes estimates.


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