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 $\delta _{1}$ 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 $R(\theta ,\delta _{1})\leq R(\theta ,\delta _{2})$ 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]

References

1 2 Abadi, Mongi; Gonzalez, Rafael C. (1992), Data Fusion in Robotics & Machine Intelligence, Academic Press, p. 227, ISBN 9780323138352 .

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