The Asymptotically Unbiased Prior Distribution

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