Estimating hidden population size from a single respondent-driven sampling survey

This work is concerned with the estimation of hard-to-reach population sizes using a single respondent-driven sampling (RDS) survey, a variant of chain-referral sampling that leverages social relationships to reach members of a hidden population. The popularity of RDS as a standard approach for surveying hidden populations brings theoretical and methodological challenges regarding the estimation of population sizes, mainly for public health purposes. This paper proposes a frequentist, model-based framework for estimating the size of a hidden population using a network-based approach. An optimization algorithm is proposed for obtaining the identification region of the target parameter when model assumptions are violated. We characterize the asymptotic behavior of our proposed methodology and assess its finite sample performance under departures from model assumptions.