Asymptotic Normmality of Maximum Likelihood Estimators Obtained from Normally Distributed but Dependent Observations

Abstract

In this article we aim to establish intuitively appealing and verifiable conditions for the first-order efficiency and asymptotic normality of ML estimators in a multi-parameter framework, assuming joint normality but neither the independence nor the identical distribution of the observations. We present five theorems (and a large number of lemmas and propositions), each being a special case of its predecessor.