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Decision function

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decision procedure, statistical decision rule

A rule according to which statistical decisions are made on the basis of observations obtained.

Let be a random variable that takes values in a sampling space , , and let be the set of all possible decisions that can be taken relative to the parameter with respect to a realization of . According to the accepted terminology in mathematical statistics and the theory of games, any -measurable transformation of the space of realizations of into the set of possible decisions is called a decision function. For example, in the statistical estimation of the parameter any point estimator is a decision function. A basic problem in statistics in obtaining statistical conclusions is the choice of a decision function that minimizes the risk

relative to the loss function used.

The concept of a decision function is a basic concept in the theory of statistical decision functions as developed by A. Wald.

References

[1] N.N. Chentsov, "Statistical decision laws and optimal inference" , Amer. Math. Soc. (1982) (Translated from Russian)
[2] A. Wald, "Statistical decision functions" , Wiley (1950)


Comments

Cf. also Statistical decision theory.

References

[a1] J.O. Berger, "Statistical decision theory. Foundations, concepts and models" , Springer (1980)
How to Cite This Entry:
Decision function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Decision_function&oldid=39493
This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article