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 δ 1 and δ 2 be two decision rules, and let R ( θ , δ ) be the risk of rule δ for parameter θ . The decision rule δ 1 is said to dominate the rule δ 2 if R ( θ , δ 1 ) ≤ R ( θ , δ 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.