Dominating decision rule explained

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

\delta _{1} and \delta _{2} be two decision rules, and let R(\theta, \delta) be the risk of rule \delta for parameter \theta . The decision rule \delta _{1} is said to dominate the rule \delta _{2} if R(\theta,\delta _{1)\le} R(\theta,\delta _{2)} for all \theta , and the inequality is strict for some \theta .^[1]

This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.^[1]

Notes and References

1. .