Let $\backslash delta\_1$ and $\backslash delta\_2$ be two decision rules, and let $R(\backslash theta,\; \backslash delta)$ be the risk of rule $\backslash delta$ for parameter $\backslash theta$.

The decision rule $\backslash delta\_1$ is said to dominate the rule $\backslash delta\_2$ if $R(\backslash theta,\backslash delta\_1)\backslash le\; R(\backslash theta,\backslash delta\_2)$ for all $\backslash theta$, and the inequality is strict for some $\backslash theta$.

See also Admissible decision rule.

Decision theory

Dominanta decida regulo