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 and be two decision rules, and let be the risk of rule for parameter . The decision rule is said to dominate the rule if for all, and the inequality is strict for some . This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.