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

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

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    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.

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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-306.

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    Length: 23 pages
    Date of creation: Oct 2004
    Date of revision:
    Handle: RePEc:tky:fseres:2004cf306

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