On the Asymptotic Normality of the Maximum Likelihood Estimator With Dependent Observations

In this paper we study the asymptotic normality of the maximum likelihood estimator obtained from dependent observations. Our conditions are somewhat weaker than usual, in that we do not require convergences in probability to be uniform or third-order derivatives to exist; moreover, the conditions will appear to be readily verifiable. This paper builds on Witting and Nolle's result concerning the asymptotic normality of the maximum likelihood estimator obtained from independent and identically distributed observations, and on a martingale theorem by McLeish