Estimating Population Size With Link-Tracing Sampling

ABSTRACT

We present a new design and method for estimating the size of a hidden population best reached through a link-tracing design. The design is based on selecting initial samples at random and then adaptively tracing links to add new members. The inferential procedure involves the Rao–Blackwell theorem applied to a sufficient statistic markedly different from the usual one that arises in sampling from a finite population. The strategy involves a combination of link-tracing and mark-recapture estimation methods. An empirical application is described. The result demonstrates that the strategy can efficiently incorporate adaptively selected members of the sample into the inferential procedure. Supplementary materials for this article are available online.

Keywords:

• Adaptive sampling
• Design-based inference
• Mark-recapture
• Rao–Blackwell method
• Unknown population size

Supplementary Materials

The supplementary materials detail the adaptive sampling design that allows random jumps at intermediate stages of the sample selection procedure; provide a sufficiency result for the generalized adaptive sampling design; provide a discussion of sample reorderings consistent with the sufficient statistic; and present simulation study results for mark-recapture estimators based on a M_h heterogeneity capture model applied to the empirical population.

Acknowledgments

The authors wish to thank Laura Cowen, Charmaine Dean, Maren Hansen, Chris Henry, Kim Huynh, Richard Lockhart, Louis-Paul Rivest, Carl Schwarz, and Jason Sutherland for their helpful comments. The authors also wish to thank John Potterat and Steve Muth for making the Colorado Springs data available. All views expressed in this article are solely those of the authors and should not be attributed to the Bank of Canada.

Funding

This work was supported through a Natural Sciences and Engineering Research Council Postgraduate Scholarship D and a Discovery Grant.