Horvitz-Thompson estimator under partial information with an application to network degree distribution

Abstract

We present an extension of the Horvitz-Thompson estimator for estimating the total number of sets of a given size within a population. We study the limitations of the Horvitz-Thompson under partial information where we have a sample of population elements rather than of sets. The developed estimator is the chained Horvitz-Thompson. We apply this estimator to the estimate the network degree distribution to be used under probability sampling designs, in particular, induced subgraph and incident subgraph. Finally, we present Monte Carlo simulations to assess the accuracy of the proposed estimator.