The Annals of Statistics

Admissible Representation of Asymptotically Optimal Estimates

H. Strasser

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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.

Article information

Source
Ann. Statist., Volume 6, Number 4 (1978), 867-881.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344260

Digital Object Identifier
doi:10.1214/aos/1176344260

Mathematical Reviews number (MathSciNet)
MR518879

Zentralblatt MATH identifier
0378.62033

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62F15: Bayesian inference 62F20 62E20: Asymptotic distribution theory 62C15: Admissibility

Keywords
Asymptotic expansions posterior distributions median unbiased estimates Bayes estimates

Citation

Strasser, H. Admissible Representation of Asymptotically Optimal Estimates. Ann. Statist. 6 (1978), no. 4, 867--881. doi:10.1214/aos/1176344260. https://projecteuclid.org/euclid.aos/1176344260


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