On an admissibility problem involving the moment generating function of the lognormal distribution

A new location invariant loss function is considered and the best invariant estimator of normal mean is obtained. This estimator is a function of the moment generating function of the lognormal distribution. The admissibility is studied of a class of linear estimators of the form cX + d, where X ∼ N(θ, σ <Superscript>2</Superscript>), with θ unknown and σ <Superscript>2</Superscript> known. This yields the admissibility of the best invariant estimator of θ. Copyright Springer-Verlag 2003