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We propose Horvitz-Thompson-like and Hajek-like estimators of the total andmean of the values of a variable of interest associated with the elements of ahard-to-reach population sampled by the variant of link-tracing samplingproposed by Felix-Medina and Thompson (2004). As examples of this type ofpopulation are drug users, homeless people and sex workers. In this samplingvariant, a frame of venues or places where the members of the population tendto gather, such as parks and bars, is constructed. The frame is not assumed tocover the whole population. An initial cluster sample of elements is selectedfrom the frame, where the clusters are the venues, and the elements in theinitial sample are asked to name their contacts who are also members of thepopulation. The sample size is increased by including in the sample the namedelements who are not in the initial sample. The proposed estimators do not usedesign-based inclusion probabilities, but model-based inclusion probabilitieswhich are derived from a model proposed by Felix-Medina et al. (2015) and areestimated by maximum likelihood estimators. The inclusion probabilities areassumed to be heterogeneous, that is, that they depend on the sampled people.Estimates of the variances of the proposed estimators are obtained by bootstrapand they are used to construct confidence intervals of the totals and means.The performance of the proposed estimators and confidence intervals isevaluated by two numerical studies, one of them based on real data, and theresults show that their performance is acceptable.

Combining Cluster Sampling and Link-Tracing Sampling to Estimate Totals  and Means of Hidden Populations in Presence of Heterogeneous Probabilities of  Links