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Connecting Correction Methods for Linkage Error in Capture-Recapture

Author

Listed:
  • de Wolf Peter-Paul

    (Statistics Netherlands, P.O.Box 24500, 2490 HA The Hague, The Netherlands.)

  • van der Laan Jan

    (Statistics Netherlands, P.O.Box 24500, 2490 HA The Hague, The Netherlands.)

  • Zult Daan

    (Statistics Netherlands, P.O.Box 24500, 2490 HA The Hague, The Netherlands.)

Abstract
A commonly known problem in population size estimation using registers, is that registers do not necessarily cover the whole population. This may be because they intend to cover part of the population (e.g., students), due to administrative delay or because part of the target population is not registered by default (e.g., illegal persons). One of the methods to estimate the population size in the presence of undercount is the capture-recapture method that combines the information of two or more samples. In the context of census estimation registers are used instead of samples. However, the method assumes that perfect linkage between the registers can be achieved. It is known that this assumption is often violated.In the setting of evaluating the population coverage of a census using a post-enumeration survey, a correction for linkage error was proposed. That correction was later generalized by relaxing some of the newly introduced conditions. However, the new correction method still implicitly assumed that the two registers are of equal size. We introduce a further generalization that includes both previously mentioned correction methods and at the same time deals with registers of different sizes. Specific parameter settings will correspond to the different correction methods. We show that the parameters of each method can be chosen such that the resulting estimates all equal the traditional Petersen estimate (1896) that would theoretically be obtained under truly perfect linkage.

Suggested Citation

  • de Wolf Peter-Paul & van der Laan Jan & Zult Daan, 2019. "Connecting Correction Methods for Linkage Error in Capture-Recapture," Journal of Official Statistics, Sciendo, vol. 35(3), pages 577-597, September.
    • Handle: RePEc:vrs:offsta:v:35:y:2019:i:3:p:577-597:n:4
    DOI: 10.2478/jos-2019-0024
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    References listed on IDEAS

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    1. Di Consiglio Loredana & Tuoto Tiziana, 2015. "Coverage Evaluation on Probabilistically Linked Data," Journal of Official Statistics, Sciendo, vol. 31(3), pages 415-429, September.
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