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Connecting Correction Methods for Linkage Error in Capture-Recapture
Journal of Official Statistics ( IF 0.5 ) Pub Date : 2019-09-01 , DOI: 10.2478/jos-2019-0024
Peter-Paul de Wolf 1 , Jan van der Laan 1 , Daan Zult 1
Affiliation  

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.

中文翻译:

捕获-重新捕获中链接错误的连接校正方法

摘要在使用寄存器进行人口规模估计时,一个众所周知的普遍问题是寄存器不一定覆盖整个人口。这可能是因为他们由于行政上的延误而打算覆盖部分人口(例如学生),或者因为默认情况下未对目标人口的一部分进行注册(例如非法人)。在存在计数不足的情况下估计种群规模的方法之一是结合两个或多个样本信息的捕获-捕获方法。在人口普查的背景下,使用寄存器代替样本。但是,该方法假定可以实现寄存器之间的完美链接。众所周知,这种假设经常被违反。在使用枚举后调查评估人口普查的人口覆盖范围时,提出了一种校正链接错误的方法。后来通过放宽一些新引入的条件来概括该更正。但是,新的校正方法仍隐式假定两个寄存器的大小相等。我们引入了进一步的概括,其中包括前面提到的两种校正方法,同时处理了不同大小的寄存器。特定的参数设置将对应于不同的校正方法。我们表明,可以选择每种方法的参数,以使所得到的估计值都等于传统的Petersen估计值(1896),该估计值理论上是在真正完美的链接下获得的。新的校正方法仍隐含地假定两个寄存器的大小相等。我们引入了进一步的概括,其中包括前面提到的两种校正方法,同时处理了不同大小的寄存器。特定的参数设置将对应于不同的校正方法。我们表明,可以选择每种方法的参数,以使所得到的估计值都等于传统的Petersen估计值(1896),该估计值理论上是在真正完美的链接下获得的。新的校正方法仍然隐式假定两个寄存器的大小相等。我们引入了进一步的概括,其中包括前面提到的两种校正方法,同时处理了不同大小的寄存器。特定的参数设置将对应于不同的校正方法。我们表明,可以选择每种方法的参数,以使所得到的估计值都等于传统的Petersen估计值(1896),该估计值理论上是在真正完美的链接下获得的。
更新日期:2019-09-01
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