Asymptotics of maximum likelihood estimators based on Markov chain Monte Carlo methods

In complex statistical models, in which exact computation of the likelihood is intractable, Monte Carlo methods can be applied to approximate maximum estimates. this paper we consider approximation obtained via Markov chain Carlo. We prove consistency and asymptotic normality resulting estimator, when both sample sizes (the initial one) tend infinity. Our results models with intractable normalizing constants missing data models. also investigate properties estimators numerical experiments.