Estimating Population Size from a Privatized Network Sample

Link-tracing designs, such as respondent-driven sampling (RDS), are extensively used to perform inference on marginalized and hard-to-reach populations. Privatized network sampling (PNS), where the identities of each subject's connections are collected in a manner that preserves their privacy, is an extension of RDS that admits new inferential procedures. We derive two new population size estimators for PNS studies. We explore their performance in both simulated and empirically collected network datasets and find them to have reduced bias along with considerably lower variance than previously developed estimators.