Estimation of a Mean of a Normal Distribution with a Bounded Coefficient of Variation

Tatsuya Kubokawa
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-306, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: 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.

Pages: 23 pages
Date: 2004-10
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2004cf306

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