## The Annals of Statistics

### Admissible Representation of Asymptotically Optimal Estimates

H. Strasser

#### 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

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