Minimax estimator

<p>In statistical <a href="/facts/Decision_theory/TbXcQX0v">decision theory</a>, a minimax estimator 
  
    
      
        
          δ
          
            M
          
        
        
        
      
    
    {\displaystyle \delta ^{M}\,\!}
  
 is an estimator which performs best in the worst possible case allowed in a problem. With problems of estimating a deterministic parameter (vector) 
  
    
      
        θ
        ∈
        Θ
      
    
    {\displaystyle \theta \in \Theta }
  
 from observations 
  
    
      
        x
        ∈
        
          
            X
          
        
        ,
      
    
    {\displaystyle x\in {\mathcal {X}},}
  
 an <a href="/facts/Estimator/CbkjcKvN">estimator</a> (estimation rule) 
  
    
      
        
          δ
          
            M
          
        
        
        
      
    
    {\displaystyle \delta ^{M}\,\!}
  
 is called <a href="/facts/Minimax/GcCTKutW">minimax</a> if its maximal <a href="/facts/Risk_function/xv5ozuhl">risk</a> is minimal among all estimators of 
  
    
      
        θ
        
        
      
    
    {\displaystyle \theta \,\!}
  
. 
</p>

Minimax estimator open-in-new

Minimax estimator