Loss function

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In a problem of statistical decision making, a non-negative function indicating the loss (cost) to an experimenter given a particular state of the world and a particular decision. Let be a random variable taking values in a sample space , , and let be the space of all possible decisions that can be taken on the basis of an observed . In the theory of statistical decision functions, any non-negative function defined on is called a loss function. The value of a loss function at an arbitrary point is interpreted as the cost incurred by taking a decision , when the true parameter is , .


[1] A. Wald, "Statistical decision functions" , Wiley (1950)
[2] E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986)



[a1] J.O. Berger, "Statistical decision theory and Bayesian analysis" , Springer (1985)
How to Cite This Entry:
Loss function. M.S. Nikulin (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098