Maximum likelihood estimation for discrete exponential families and random graphs

2019/11/29 by Bogdan, Krzysztof, Bosy, Michał, Skalski, Tomasz · 1 citation
#05C80 #62H12 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1911.13143

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.

Cited by

• Level sets and maximum likelihood estimation for the Ising model

Related

• Existence of maximum likelihood estimates in exponential random graph models
• On the Geometry of Discrete Exponential Families with Application to Exponential Random Graph Models
• Computationally efficient likelihood inference in exponential families\n when the maximum likelihood estimator does not exist
• Stein's method of moment estimators for local dependency exponential random graph models
• Maximum entropy distributions on graphs