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

Ludwig Baringhaus

Scandinavian Journal of Statistics, 2003, vol. 30, issue 3, 597-608

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.

Date: 2003
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https://doi.org/10.1111/1467-9469.00351

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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:30:y:2003:i:3:p:597-608

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