Estimation of Finite Population Proportions for Small Areas - A Statistical Data Integration Approach

Empirically best prediction (EBP) is used to estimate proportions in small or incomplete populations, but often encounters practical limitations such as missing auxiliary variables or incomplete data linkages.

The proposed approach replaces the limited population frame with a large sample with many auxiliary variables, but lacks the target variable.

A model is estimated on a small sample to impute the outcome variable for the large sample and calculate weighted proportions.

To improve the estimation quality, a new adjusted maximum likelihood method is developed that avoids variance estimation problems.

In addition, a bootstrap-based error estimator and an efficient expectation maximization algorithm are introduced, and the method is demonstrated using election forecasts for small regions.