Capture–Recapture Sampling and Indirect Sampling

Pierre Lavallée, Louis-Paul Rivest

Abstract:
Capture–recapture sampling is used to estimate the total number of units in a population of unknown size. It involves two samples selected independently in the target population. The Petersen estimator for the population size depends on the frequencies of the units appearing in the first, the second or both samples. This article considers a generalisation of capture–recapture sampling to cases where the two samples are selected using indirect sampling (Lavallée 2002; 2007). The sampling frames for the two samples differ from the target population and the generalised weight share method has to be used to determine the sampling weights of units selected in the population through this indirect method. A generalisation of the Petersen estimator to such an indirect sampling scheme is proposed. The sampling properties of this new estimator are investigated. Its application is illustrated through simulations and by discussing two surveys where it could be used.

Keywords:
Petersen estimator, generalised weight share method, population size, administrative files