Maximum likelihood estimation for discrete exponential families and random graphs

Abstract

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application, we point out the size of independent identically distributed samples for which the maximum likelihood estimator exists with high probability.

21 pages, minor editorial changes, added connections to the criterion of Barndorff-Nielsen and linear programming