Trimmed dual system estimation

The so-called dual system estimator (DSE) is a standard capture-recapture method for census under-count assessment. However, there are many situations where the list enumerations also suffer from over-counting (i.e. erroneous enumeration). The standard DSE is then biased in such situations. In this chapter we propose and study a trimmed dual system estimator (TDSE) that can be used to explore, reduce and potentially remove, the bias of the standard DSE in the presence of erroneous enumeration. It is shown that, as long as the trimming is more effective at picking out erroneous records than simple random sampling, and that one does not trim more than the actual number of erroneous records, the TDSE can be expected to be less biased than the na\"{i}ve DSE that overlooks the erroneous enumerations. Diagnostics are provided for the stopping rule, i.e. when to stop the trimming. The approach is applied in a project at CSO, Ireland, to produce population counts from administrative data sources. Such population counts will provide a critical first step for countries without a Central Population Register to transition from a traditional Census model to one based on administrative data sources