Asymptotic Minimax and Admissibility in Estimation

摘要

A sequence of general experiments is considered over a k-dimensional parameter. Under conditions of local asymptotic normality (LAN) of the families of distributions, we prove that, from the point of view of the local asymptotic minimax, there is a lower bound, which may be obtained only if the estimator has certain linear relation to the derivative of the likelihood function. This entails asymptotic normality with Fisher's variance. Conditions LAN are proved under the sole condition of continuity of Fisher's information. (Author)