Many of the available methods for estimating small-area parameters are model-based approaches in which auxiliary variables are used to predict the variable of interest. For models that are nonlinear, prediction is not straightforward. MacGibbon and Tomberlin and Farrell, MacGibbon, and Tomberlin have proposed approaches that require microdata for all individuals in a small area. In this article, we develop a method, based on a second-order Taylor-series expansion to obtain model-based predictions, that requires only local-area summary statistics for both continuous and categorical auxiliary variables. The methodology is evaluated using data based on a U.S. Census.

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Journal of Business and Economic Statistics
Sprott School of Business

Farrell, P, MacGibbon, B. (Brenda), & Tomberlin, T.J. (1997). Empirical bayes small-area estimation using logistic regression models and summary statistics. Journal of Business and Economic Statistics, 15(1), 101–108. doi:10.1080/07350015.1997.10524692