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:

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

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.

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