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August, 1965 The Asymptotically Unbiased Prior Distribution
J. A. Hartigan
Ann. Math. Statist. 36(4): 1137-1152 (August, 1965). DOI: 10.1214/aoms/1177699988


In estimation of a real valued parameter $\theta$, using observations from the probability density $f(x \mid \theta)$, and using loss function $L(\theta, \phi)$, the prior density which minimizes asymptotic bias of the associated estimator is shown to be $J(\theta) = \varepsilon((\partial/\partial\theta) \log f)^2/\lbrack(\partial^2/\partial\phi^2)L(\theta, \phi)\rbrack^{\frac{1}{2}}_{\phi = \theta}$. Results are also given for estimation in higher dimensions.


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J. A. Hartigan. "The Asymptotically Unbiased Prior Distribution." Ann. Math. Statist. 36 (4) 1137 - 1152, August, 1965.


Published: August, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0133.42106
MathSciNet: MR176539
Digital Object Identifier: 10.1214/aoms/1177699988

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 4 • August, 1965
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