Capture-recapture models for official statistics in presence of out-of-scope units: an overview

During the last years, National Statistics Institutes have been exploring the possibility to produce statistics based on administrative data only. In particular, the interest in populations. size estimation is increasing. However, some issues naturally emerge since the aims of those who collect data and those who use them differ. On the one hand, it is very likely to have out-ofscope units in the datasets. On the other hand, some units that belong to the target population are not observed. In practice, this is the case of incomplete contingency tables that include some overcounts. The aim of this paper is to review the main and most recent literature dealing with the population size estimation problem, with an insight on the overcoverage issue.