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Abstract:
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Graph sampling provides a statistical approach to study real graphs, which can be of interest in numerous investigations. There have been significant contributions to the existing graph sampling theory. However, a general approach to graph sampling which also unifies the existing unconventional sampling methods, which may be envisaged as graph sampling problems, including indirect, network and adaptive cluster sampling, as well as arbitrary T-stage snowball sampling, is non-existent in the literature. We propose a bipartite incident graph sampling (BIGS) as a feasible representation of graph sampling from arbitrary finite graphs and a unified approach to a large number of graph sampling situations. We establish the sufficient and necessary conditions under which the BIGS is feasible for various graph sampling methods. Under a feasible BIGS, two types of design-unbiased estimators, the Horvitz-Thompson estimator and the Hansen-Hurwitz type of estimators, can be applied. A general result on the relative efficiency of the two types of estimators is obtained. Some numerical results based on a limited simulation study illustrating the feasibility of the proposed approach are presented.
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