CIRJE-F-306. Kubokawa, Tatsuya, "Estimation of a Mean of a Normal Distribution with a Bounded Coefficient of Variation", October 2004.

The estimation of a mean of a normal distribution with an unknown variance is addressed under the restriction that the coefficient of variation is within a bounded interval. The paper constructs a class of estimators improving on the best location-scale equivariant estimator of the mean. It is demonstrated the class includes three typical estimators: the Bayes estimator against the uniform prior over the restricted region, the Bayes estimator against the prior putting mass on the boundary, and a truncated estimator. The non-minimaxity of the best location-scale equivariant estimator is shown in the general location-scale family. When another type of restriction is treated, however, we have a different story that the best location-scale equivariant estimator remains minimax.