Risk_function

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:

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

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