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Abstract:
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Generally in network analysis the implicit assumption is made that we observe a network (or, equivalently, its adjacency matrix) in its entirety. Often, however, it is the case that relational information is observed on only a portion of a complex system being studied, and the network resulting from such measurements may be thought of as a sample from a larger underlying network. In fact, arguably sampled networks may be more the rule than the exception in practice. Yet sampling in networks, and the corresponding statistical inference problems that arise, have to date been noticeably less studied than, for example, network modeling. In this talk, I focus on challenges posed by the problem of estimation of network characteristics under network sampling, with an emphasis on problems involving vertex degrees. Following some necessary background, I will present results on three versions of degree estimation: estimation of the mean degree, of the degree distribution, and of the individual vertex degree. The problems exhibit substantially increasing difficulty as the scale of the structure of interest goes from global to local.
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