Risk function

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This article is about the mathematical definition of risk in statistical decision theory. For a more general discussion of concepts and definitions of risk, see the main article Risk.

In decision theory, the risk of an estimator δ(x) to be calculated from some observables x is the expected value of the loss function as a function on the unknown underlying state of nature θ:

$R(\theta,\delta) = \int L(\theta,\delta(x)) f(x|\theta)\,dx$ .

[edit] References

James O. Berger Statistical Decision Theory and Bayesian Analysis. Second Edition. Springer-Verlag, 1980, 1985. ISBN 0-387-96098-8.
Morris De Groot Optimal Statistical Decisions. Wiley Classics Library. 2004. (Originally published 1970.) ISBN 0-471-68029-X.
Christian P. Robert The Bayesian Choice. Springer-Verlag 1994. ISBN 3-540-94296-3.