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On Unbiased Estimation of Positive Integral Powers of the Natural Parameter in Exponential Families |
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| Authors: | Ludwig Baringhaus |
| Institution: | Universität Hannover |
| 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. |
| Keywords: | exponential families natural parameter of an exponential family unbiased estimation |