1994 | OriginalPaper | Buchkapitel
More on Incomplete and Boundedly Complete Families of Distributions
verfasst von : Wassily Hoeffding
Erschienen in: The Collected Works of Wassily Hoeffding
Verlag: Springer New York
Enthalten in: Professional Book Archive
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Let 2. be a family of distributions (probability measures) on a measurable space [Y,B) and let r be a group of B-measurable transformations of Y. The family 2. is said to be complete relative to r if no nontrivial r-invariant unbiased estimator of zero for 2. exists. (A function is called Γ-invariant if it is invariant under all transformations in Γ.) The family 2. is said to be boundedly complete relative to Γ if no bounded nontrivial Γ-invariant unbiased estimator of zero for 2. exists.