A probability model for census adjustment

The census can be adjusted using capture-recapture techniques: capture in the census, recapture in a special Post Enumeration Survey (PES) done after the census. The population is estimated using the Dual System Estimator (DSE). Estimates are made separately for demographic groups called post strata; adjustment factors are then applied to these demographic groups within small geographic areas. We offer a probability model for this process, in which several sources of error can be distinguished. In this model, correlation bias arises from behavioral differences between persons counted in the census and persons missed by the census. The first group may on the whole be more likely to respond to the PES: if so, the DSE will be systematically too low, and that is an example of correlation bias. Correlation bias is distinguished from heterogeneity, which occurs if the census has a higher capture rate in some geographic areas than others. Finally, ratio estimator bias and variance are considered. The objective is to clarify the probabilistic foundations of the DSE, and the definitions of certain terms widely used in discussing that estimator.