Properties of Census Dual System Population Size Estimators

We study parametric and non‐parametric approaches for assessing the accuracy and coverage of a population census based on dual system surveys. The two parametric approaches being considered are post‐stratification and logistic regression, which have been or will be implemented for the US Census dual system surveys. We show that the parametric model‐based approaches are generally biased unless the model is correctly specified. We then study a local post‐stratification approach based on a non‐parametric kernel estimate of the Census enumeration functions. We illustrate that the non‐parametric approach avoids the risk of model mis‐specification and is consistent under relatively weak conditions. The performances of these estimators are evaluated numerically via simulation studies and an empirical analysis based on the 2000 US Census post‐enumeration survey data.