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July, 1978 Admissible Representation of Asymptotically Optimal Estimates
H. Strasser
Ann. Statist. 6(4): 867-881 (July, 1978). DOI: 10.1214/aos/1176344260

Abstract

A sequence of medians of posterior distributions is approximately median unbiased of order $o(n^{-1}) \operatorname{iff}$ the prior density is equal to the square root of Fisher's information function. It is shown that in this case the sequence of medians of posterior distributions is even an optimum sequence of estimates within the class of all estimator sequences being approximately median unbiased of order $o(n^{-1}).$ The result is proved by showing equivalence with an expansion of an optimum sequence given by Pfanzagl. In the case of a location parameter family the Bayesian representation is admissible.

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H. Strasser. "Admissible Representation of Asymptotically Optimal Estimates." Ann. Statist. 6 (4) 867 - 881, July, 1978. https://doi.org/10.1214/aos/1176344260

Information

Published: July, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62033
MathSciNet: MR518879
Digital Object Identifier: 10.1214/aos/1176344260

Subjects:
Primary: 62F10
Secondary: 62C15 , 62E20 , 62F15 , 62F20

Keywords: asymptotic expansions , Bayes estimates , median unbiased estimates , posterior distributions

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 4 • July, 1978
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