ASYMPTOTIC MINIMAX AND ADMISSIBILITY IN ESTIMATION.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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 Fishers variance. Conditions LAN are proved under the sole condition of continuity of Fishers information. Author
- Statistics and Probability