Title: Consistent maximum likelihood estimation of random graph models with local dependence and growing neighborhoods
Authors: Michael Schweinberger - Department of Statistics, Rice University (United States) [presenting]
Jonathan Stewart - Rice University (United States)
Abstract: In general, statistical inference for exponential-family random graph models of dependent random graphs given a single observation of a random graph is problematic. We show that statistical inference for exponential-family random graph models holds promise as long as models are endowed with a suitable form of additional structure. We consider a simple and common form of additional structure called multilevel structure. To demonstrate that exponential-family random graph models with multilevel structure are amenable to statistical inference, we develop the first concentration and consistency results covering maximum likelihood estimators of a wide range of full and non-full, curved exponential-family random graph models with local dependence and natural parameter vectors of increasing dimension. In addition, we show that multilevel structure facilitates local computing of maximum likelihood estimators and in doing so reduces computing time. Taken together, these results suggest that exponential-family random graph models with multilevel structure constitute a promising direction of statistical network analysis.