Introduction to Levit (1974) On the Optimality of Some Statistical Estimates
The intuitive appeal of maximum likelihood estimators (equivalently: Bayes estimators with uniform prior) made it seem easy to establish their optimality as a mathematical theorem, at least asymptotically. A first result in this direction is due to Edgeworth (1908), who proves the maximum likelihood estimator of a location parameter to be asymptotically optimal among all estimators which are solutions to estimating equations. Various attempts by Fisher did not achieve much more than generalizing Edgeworth’s result from location parameters to arbitrary one-dimensional parameters. It took surprisingly long to realize that the idea of asymptotic efficiency as originally conceived was too naive. The reason for this is, perhaps, that the admirable intuition of the early statisticians was not kept in control by the requirement of mathematical rigor.
KeywordsLoss Function Statistical Estimate Maximum Likelihood Estimator Tangent Cone Minimax Theorem
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