  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. To illustrate the usefulness of these results beyond their obvious
use, an example shows that in certain cases the sample average is preferable to
inverse probability weighting. We provide a test statistic to distinguish
between these two cases.
