Estimation of Vertex Degrees in a Sampled Network

The need to produce accurate estimates of vertex degree in a large network, based on observation of a subnetwork, arises in a number of practical settings. We study a formalized version of this problem, wherein the goal is, given a randomly sampled subnetwork from a large parent network, to estimate the actual degree of the sampled nodes. Depending on the sampling scheme, trivial method of moments estimators (MMEs) can be used. However, the MME is not expected, in general, to use all relevant network information. In this study, we propose a handful of novel estimators derived from a risk-theoretic perspective, which make more sophisticated use of the information in the sampled network. Theoretical assessment of the new estimators characterizes under what conditions they can offer improvement over the MME, while numerical comparisons show that when such improvement obtains, it can be substantial. Illustration is provided on a human trafficking network.