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On Unbiased Estimation of Positive Integral Powers of the Natural Parameter in Exponential Families

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  • Ludwig Baringhaus

Abstract

We explore the structure of one‐parameter exponential families admitting an unbiased estimator for a positive integral power of the natural parameter. It is seen that only exponential families dominated by Lebesgue measure can have this property. It is outlined that similar results can be obtained for other functions of the natural parameter.

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  • Ludwig Baringhaus, 2003. "On Unbiased Estimation of Positive Integral Powers of the Natural Parameter in Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 597-608, September.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:3:p:597-608
    DOI: 10.1111/1467-9469.00351
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