Empirical Bayes Small-Area Estimation Using Logistic Regression Models and Summary Statistics.

Many available methods for estimating small area parameters are model-based, where auxiliary variables are used to predict the variable of interest. For nonlinear models, prediction is not straightforward. MacGibbon and Tomberlin (1989) and Farrell, MacGibbon, and Tomberlin (1994) have proposed methods which require micro-data for each individual in a small area. Here, the authors use a second-order Taylor series expansion to obtain model-based predictions which only require local area summary statistics in the case of either continuous or categorical auxiliary variables. The methodology is evaluated using U.S. census data.