The Capture-recapture method is a well-known solution for evaluating the unknown size of a population. Administrative data represent sources of independent counts of a population and can be jointly exploited for applying the capture-recapture method. Of course, administrative sources are affected by over- or undercoverage when considered separately. The standard Petersen approach is based on strong assumptions, including perfect record linkage between lists. In reality, record linkage results can be affected by errors. A simple method for achieving linkage error-unbiased population total estimates is proposed in Ding and Fienberg (1994). In this article, an extension of the Ding and Fienberg model by relaxing their conditions is proposed. The procedures are illustrated for estimating the total number of road casualties, on the basis of a probabilistic record linkage between two administrative data sources. Moreover, a simulation study is developed, providing evidence that the adjusted estimator always performs better than the Petersen estimator.
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