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On Unbiased Estimation of Positive Integral Powers of the Natural Parameter in Exponential Families
Author(s) -
Baringhaus Ludwig
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00351
Subject(s) - mathematics , exponential family , natural exponential family , exponential function , estimator , gamma distribution , measure (data warehouse) , property (philosophy) , statistics , mathematical analysis , philosophy , epistemology , database , computer science
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.