Capture-recapture methods in the presence of linkage errors

This chapter explains different proposals that adjust the capture-recapture estimation by explicitly taking into account the linkage errors. It reviews some common frequentist and Bayesian record linkage approaches and estimation of the associated of linkage errors. The chapter describes the probabilistic record linkage frameworks, mainly in order to formalize the definition and the estimation of linkage errors. The two types of linkage error, namely false links and missed matches, play a central role in adjusting statistical analysis based on linkage data, including the capture-recapture estimators. The Ding and Fienberg estimators and the Modified Ding and Fienberg estimators are both based on the assumption that linkage errors are constant overall. If the assumption holds at least in sub-groups, the estimators can be applied within strata in which the linkage error probabilities are more homogeneous than in the whole population. The chapter provides some remarks on the dual system estimator in the presence of linkage errors.