Open Access
Comparison of Experiments
David Blackwell
- Vol. 2, pp 93-102
TLDR
In this paper, it was shown that if a > and n are independent, then the combination (a, -y) > (#, y) is a sufficient statistic for a procedure equivalent to,S, a >, it is shown that a v j3.1.Abstract:
1. Summary Bohnenblust, Shapley, and Sherman [2] have introduced a method of comparing two sampling procedures or experiments; essentially their concept is that one experiment a is more informative than a second experiment ,, a v ,S, if, for every possible risk function, any risk attainable with , is also attainable with a. If a is a sufficient statistic for a procedure equivalent to ,S, a >,, it is shown that a v j3. In the case of dichotomies, the converse is proved. Whether > and v are equivalent in general is not known. Various properties of > and n are obtained, such as the following: if a > , and y is independent of both, then the combination (a, -y) > (#, y). An application to a problem in 2 X 2 tables is discussed.read more
Citations
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The Dual Theory of Choice under Risk.
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References
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Book
Theory Of The Integral
TL;DR: In this article, the integral in an abstract space is defined as the integral integral in the abstract space of the integral space of an abstract representation of a set of elements. But,
Journal ArticleDOI
Some Methods applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters
TL;DR: In this article, the main principle adopted is that of taking the standard form of a symmetric function to be a sum extending over all the cases of the typical term got by permuting the letters involved in all possible ways, whether they are different or not; and the main result reached is an inequality theorem arrived at by expressing the excess of the greater over the less in an explicitly positive form.
Journal ArticleDOI
Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics
Paul R. Halmos,L. J. Savage +1 more
TL;DR: In this article, the authors introduce the notion of pairwise sufficiency, which is a generalization of the Radon-Nikodym theorem of the Fisher-Neyman theorem.
Journal ArticleDOI
Left centralizers and isomorphisms of group algebras
TL;DR: In this paper, it was shown that in the strong operator topology, any left centralizer can be approximated by a finite linear combination of right translations, up to scalar factors of unit modulus.