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Central limit theorems for network driven sampling. (English) Zbl 1386.60144

Summary: Respondent-Driven Sampling is a popular technique for sampling hidden populations. This paper models Respondent-Driven Sampling as a Markov process indexed by a tree. Our main results show that the Volz-Heckathorn estimator is asymptotically normal below a critical threshold. The key technical difficulties stem from (i) the dependence between samples and (ii) the tree structure which characterizes the dependence. The theorems allow the growth rate of the tree to exceed one and suggest that this growth rate should not be too large.

MSC:

60G17 Sample path properties
62D05 Sampling theory, sample surveys
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