Maximum likelihood estimation for discrete exponential families and random graphs

TL;DR

This paper characterizes when the maximum likelihood estimator exists for discrete exponential families, especially in the context of random graphs, providing practical criteria and sample size insights.

Contribution

It offers a simple criterion for the existence of MLE in discrete exponential families, with applications to random graph models and sample size determination.

Findings

Criterion for MLE existence in discrete exponential families

Application to exponential models of random graphs

Sample size thresholds for high-probability MLE existence

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.