7.4 MAXIMUM LIKELIHOOD ESTIMATOR: PROPERTIES
In Section 7.4.1 we show that the maximum likelihood estimator is the best unbiased estimator under certain conditions. We show this by means of the Cramer-Rao lower bound. In Sections 7.4.2 and 7.4.3 we show the consistency and the asymptotic normality of the maximum likelihood estimator under general conditions. In Section 7.4.3 we define the concept of asymptotic efficiency, which is closely related to the Cramer-Rao lower bound. In Section 7.4.4 examples are given. To avoid mathematical complexity, some results are given without full mathematical rigor. For a rigorous discussion, see Amemiya (1985).