• 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…
1,061 Citations
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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
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
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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
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