Dominating decision rule

In decision theory, a decision rule is said to dominate another if the performance of the former is sometimes better, and never worse, than that of the latter.

Formally, let δ₁ and δ₂ be two decision rules, and let R(θ,δ) be the risk of rule δ for parameter θ. The decision rule δ₁ is said to dominate the rule δ₂ if $R(\theta,\delta_1)\le R(\theta,\delta_2)$ for all θ, and the inequality is strict for some θ.

This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.

See also

• Admissible decision rule