On the Asymptotic Properties of the Maximum-Likelihood Estimate Obtained from Dependent Observations

Summary The problem of weak consistency and asymptotic efficiency of the maximum-likelihood estimate in the case of dependent random variables (observations) is considered. A set of readily applicable conditions that ensure these properties of the maximum-likelihood estimate is presented. The conditions are expressed in terms of the probability density distribution of individual observations, conditioned upon all past observations. The connection between these conditions and the Fisher information measure is also discussed.