ON THE FIRST–ORDER EFFICIENCY AND ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS OBTAINED FROM DEPENDENT OBSERVATIONS

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Abstract
In this paper we study the first–order efficiency and asymptotic normality of the maximum likelihood estimator obtained from dependent observations. Our conditions are weaker than usual, in that we do not require convergences in probability to be uniform or third–order derivatives to exist.The 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.