kb/data/en.wikipedia.org/wiki/Dominating_decision_rule-0.md

title	chunk	source	category	tags	date_saved	instance
Dominating decision rule	1/1	https://en.wikipedia.org/wiki/Dominating_decision_rule	reference	science, encyclopedia	2026-05-05T12:22:28.121748+00:00	kb-cron

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
      
    
  

{\displaystyle \delta _{1}}

and

      δ
      
        2
      
    
  

{\displaystyle \delta _{2}}

be two decision rules, and let

    R
    (
    θ
    ,
    δ
    )
  

{\displaystyle R(\theta ,\delta )}

be the risk of rule

    δ
  

{\displaystyle \delta }

for parameter

    θ
  

{\displaystyle \theta }

. The decision rule

      δ
      
        1
      
    
  

{\displaystyle \delta _{1}}

is said to dominate the rule

      δ
      
        2
      
    
  

{\displaystyle \delta _{2}}

if

    R
    (
    θ
    ,
    
      δ
      
        1
      
    
    )
    ≤
    R
    (
    θ
    ,
    
      δ
      
        2
      
    
    )
  

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

for all

    θ
  

{\displaystyle \theta }

, and the inequality is strict for some

    θ
  

{\displaystyle \theta }

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

== References ==