ON LARGE DEVIATION EXPANSION OF DISTRIBUTION OF MAXIMUM-LIKELIHOOD ESTIMATOR AND ITS APPLICATION IN LARGE-SAMPLE ESTIMATION

For estimating an unknown parameter theta, the likelihood principle yi elds the maximum likelihood estimator. It is often favoured especially by the applied statistician, for its good properties in the large sam ple case. In this paper, a large deviation expansion for the distribut ion of the maximum likelihood estimator is obtained. The asymptotic ex pansion provides a useful tool to approximate the tail probability of the maximum likelihood estimator and to make statistical inference. Th eoretical and numerical examples are given. Numerical results show tha t the large deviation approximation performs much better than the clas sical normal approximation.