Dominating decision rule

{{Short description|Rule that is never worse and sometimes better}}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 <math>\delta_1</math> and <math>\delta_2</math> be two decision rules, and let <math>R(\theta, \delta)</math> be the risk of rule <math>\delta</math> for parameter <math>\theta</math>. The decision rule <math>\delta_1</math> is said to dominate the rule <math>\delta_2</math> if <math>R(\theta,\delta_1)\le R(\theta,\delta_2)</math> for all <math>\theta</math>, and the inequality is strict for some <math>\theta</math>.<ref name="fusion">{{citation|title=Data Fusion in Robotics & Machine Intelligence|first1=Mongi|last1=Abadi|last2=Gonzalez|first2=Rafael C.|publisher=Academic Press|year=1992|isbn=9780323138352|page=227|url=https://books.google.com/books?id=47kOwU1xvMMC&pg=PA227}}.</ref>

This defines a partial order on decision rules; the maximal elements with respect to this order are called ''admissible decision rules.''<ref name="fusion"/>

==References== {{reflist}}

{{statistics-stub}} Category:Decision theory