Weighting a Census as a Non-Probability Sample: A Doubly Robust Framework for Correcting Differential. Undercoverage in Uruguay's 2023 Census

The 2023 Uruguayan Population and Housing Census recorded a population of 3,444,451 with an estimated undercoverage of 10.3\%, a sharp departure from the country's historically high coverage. Crucially, the undercoverage was non-random: post-enumeration evidence shows omission concentrated in socioeconomically vulnerable areas, in rural territories, and among young adults. Integrating administrative records into a combined census recovered the aggregate population count but did not address the substantive problem, because administrative sources lack the roughly one hundred core census variables, exhibit institutional-visibility and urbanicity biases, and do not reconstruct households. Consequently, estimates of core variables derived from the enumerated microdata remain biased. We treat the set of effectively enumerated households as a non-probability sample of an unknown selection mechanism and construct survey weights using a doubly robust (DR) estimator that combines a response-propensity model with calibration to combined-census demographic totals. The propensity component is a segment-level response model that uses the web-questionnaire linkage rate as a proxy for contact probability; the calibration component benchmarks weights to population totals by sex, single year of age, and department. Because the DR estimator is consistent when either model is correctly specified, the framework is robust to misspecification of the unknown undercoverage mechanism. We describe the construction at the scale of more than three million records, document its effect on key social indicators, and present a variance approximation based on an equivalent stratified cluster design. Finally, we establish a generalized methodological decision framework to guide national statistical offices on optimizing non-response adjustments conditional on their available administrative registers, paradata, and post-enumeration surveys.