The Asymptotically Unbiased Prior Distribution

Abstract

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.