On estimator efficiency in stochastic processes

Abstract

It is shown, under mild regularity conditions on the random information matrix, that the maximum likelihood estimator is efficient in the sense of having asymptotically maximum probability of concentration about the true parameter value. In the case of a single parameter, the conditions are improvements of those used by Heyde (1978). The proof is based on the idea of maximum probability estimators introduced by Weiss and Wolfowitz (1967).Primary 62M99 Secondary 62F20 Maximum likelihood estimation inference from stochastic processes limiting probability of concentration