Some Problems in Minimax Point Estimation
J. L. Hodges,Erich L. Lehmann +1 more
TLDR
In this article, the problem of point estimation is considered in terms of risk functions, without the customary restriction to unbiased estimates, and it is shown that, whenever the loss is a convex function of the estimate, it suffices from the risk viewpoint to consider only nonrandomized estimates.Abstract:
In the present paper the problem of point estimation is considered in terms of risk functions, without the customary restriction to unbiased estimates. It is shown that, whenever the loss is a convex function of the estimate, it suffices from the risk viewpoint to consider only nonrandomized estimates. For a number of specific problems the minimax estimates are found explicitly, using the squared error as loss. Certain minimax prediction problems are also solved.read more
Citations
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Asymptotically Subminimax Solutions of Compound Statistical Decision Problems
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References
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Contributions to the Theory of Statistical Estimation and Testing Hypotheses
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Conditional Expectation and Unbiased Sequential Estimation
TL;DR: In this paper, it was shown that whenever there is a sufficient statistic and an unbiased estimate, not a function of $u$ only, for a parameter $\theta$, the function $E(t \mid u)$, which is a function function of u only, is an unbiased estimator with a variance smaller than that of $t.