• Corpus ID: 833805

Comparison of Experiments

@inproceedings{Blackwell1951ComparisonOE,
  title={Comparison of Experiments},
  author={David Blackwell},
  year={1951}
}
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… 

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References

SHOWING 1-7 OF 7 REFERENCES

Regularity properties of certain families of chance variables

with probability 1. The subscript n here is any positive integer. It will always be supposed that the given chance variables have expectations, so that the conditional expectations involved in the

Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics

The body of this paper is written in terms of very general and abstract ideas which have been popular in pure mathematical work on the theory of probability for the last two or three decades. It

Some Methods applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters

The methods explained here are applicable to a large number of problems relating to the symmetric algebraic functions of n letters, and the special results here deduced from them are merely specimens

Some Problems in Minimax Point Estimation

In the present paper the problem of point estimation is considered in terms of risk functions, without the customary restriction to unbiased estimates. It is shown that, whenever the loss is a convex

Left centralizers and isomorphisms of group algebras

The principal result (Theorem 1) of Part I states that, conversely, every left centralizer is a convolution with a regular measure. Important auxiliary theorems (3 and 4) furnish a characterization