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REBECCA STEORTS - Carnegie Mellon University

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” Balancing the books by benchmarking: What to do when small area estimates just don't add up”
08 November 2012 from 4:00 PM to 5:00 PM
111 Tyson Bldg.
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Small area estimation has become increasingly popular due to growing demand for such statistics. In order to produce estimates of adequate precision for these small areas, it is often necessary to borrow strength from other related areas. The resulting model-based estimates may not aggregate to the more reliable direct estimates at the higher level, which may be politically problematic. Adjusting model-based estimates to correct this problem is known as benchmarking.

We propose a general class of benchmarked Bayes estimators that can be expressed in the form of a Bayesian adjustment applicable to any estimator, linear or nonlinear. We also derive a second set of estimators under an additional constraint that benchmarks the weighted variability. We illustrate this work using U.S. Census Bureau data. Finally, we determine the excess mean squared error (MSE) from constraining the estimates through benchmarking under an empirical Bayes model, and we also _nd an asymptotically unbiased estimator of this MSE and compare it to the second-order approximation of the MSE of the EB estimator or, equivalently, of the MSE of the empirical best linear unbiased predictor (EBLUP), that was derived by Prasad and Rao (1990). Morever, using methods similar to those of Butar and Lahiri (2003), we compute a parametric bootstrap estimator of the MSE of the benchmarked EB estimator and compare it to the MSE of the benchmarked EB estimator. Finally, we illustrate our methods using data from the Small Area Income and Poverty Estimates (SAIPE) Program of the U.S. Census Bureau, and in a simulation study.

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