Abstract
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 2), with θ unknown and σ 2 known. This yields the admissibility of the best invariant estimator of θ.
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Mohammadi, L. On an admissibility problem involving the moment generating function of the lognormal distribution. Metrika 57, 63–70 (2003). https://doi.org/10.1007/s001840200199
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DOI: https://doi.org/10.1007/s001840200199