# Loss function

From Encyclopedia of Mathematics

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 , .

#### References

[1] | A. Wald, "Statistical decision functions" , Wiley (1950) |

[2] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1986) |

#### Comments

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Loss_function&oldid=13130

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098