The Asymptotically Unbiased Prior Distribution

In estimation of a real valued parameter θ, using observations from the probability density f(x θ), and using loss function L(θ, φ), the prior density which minimizes asymptotic bias of the associated estimator is shown to be J(θ) = ε((∂/∂θ) log f)²/(∂²/∂φ²)L(θ, φ)1/2φ = θ. Results are also given for estimation in higher dimensions.