Bayesian Benchmarking with Applications to Small Area Estimation

Gauri S Datta
Department of Statistics
University of Georgia

Abstract: It is well-known that small area estimation needs explicit, or at least implicit use of models. These model-based estimates can differ widely from the direct estimates, especially for areas with very low sample sizes. One potential drawback of the model-based estimates is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate, the latter being usually believed to be quite reliable. This is because the original survey was designed to achieve specified inferential accuracy at this higher level of aggregation. The problem can be more severe in the event of model failure as often there is no real check for validity of the assumed model. Moreover, an overall agreement with the direct estimates at an aggregate level may sometimes be politically necessary to convince the legislators of the utility of small area estimates.

One way to avoid this problem is the so-called `benchmarking approach' which amounts to modifying these model-based estimates so that one gets the same aggregate estimate for the larger geographical area. Currently, the most popular approach is the so-called ``raking'' or ratio adjustment method which involves multiplying all the small area estimates by a constant data-dependent factor so that the weighted total agrees with the direct estimate. To our knowledge, so far this approach has been proposed more as a convenience rather than guided by any firm statistical principle. There are alternate proposals, mostly from frequentist considerations, which meet also the aforementioned benchmarking criterion.

We propose in this talk a general class of constrained Bayes estimators which achieve as well the necessary benchmarking. Interestingly enough, many of the frequentist estimators including the raked estimators follow as special cases of our general result. In the process, some deficiency of the raked estimators will be pointed out. Explicit Bayes estimators are derived which benchmark the weighted mean or both the weighted mean and variability.

Note: There will be refreshments in the lounge (MP 422) before the event. If you would like to meet with the speaker, please send email to junpark@umbc.edu.