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Statistical synthetic estimation, a technique widely suggested as a method for carrying down estimates to local levels can be shown to be a member of more general classes of estimators. It would then seem to follow that, by using information in the data, there would exist estimators that could select members of these classes based on this information, and that these estimators would outperform statistical synthetic estimation. We argue that these estimators are sometimes unavailable, and if they were available, would provide only modest improvements over the performance of the statistical synthetic estimator.
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