Asymptotics of Monte Carlo maximum likelihood estimators

TL;DR

This paper analyzes the asymptotic behavior of Monte Carlo maximum likelihood estimators in models with intractable constants, demonstrating their normality under certain conditions.

Contribution

It provides a rigorous theoretical framework for the asymptotic normality of Monte Carlo MLEs considering multiple sources of randomness.

Findings

Proves asymptotic normality of Monte Carlo MLEs

Handles models with intractable norming constants

Considers both initial sample and simulation randomness

Abstract

We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo simulations) and prove asymptotical normality of the estimator.