Efficient Likelihood Estimators

If X 1, ., X n are identically and independently distributed, then as n . ., there exists under suitable regularity conditions a sequence of solutions of the likelihood equation that is consistent and asymptotically efficient.However, this consistent solution is not necessarily the maximum likelihood estimate.Likelihood estimation should therefore emphasize the determination of a consistent sequence of solutions of the likelihood equations rather than maximizing the likelihood.The issues are illustrated on some examples.