Minimax estimator
![MSE of maximum likelihood estimator versus James–Stein estimator](/Images/godic/202501/27/MSE_of_ML_vs_JS2751.png")
In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) ![\theta \in \Theta](/Images/godic/202501/27/3b736679c7ca4c4a9b3031869c008e932751.png")
from observations ![x \in \mathcal{X},](/Images/godic/202501/27/25c273b0cf72166de7827f4e0d4198d82751.png")
an estimator (estimation rule) ![\delta^M \,\!](/Images/godic/202501/27/8025b110c47841185e72b64a472d36c02751.png")
is called minimax if its maximal risk is minimal among all estimators of ![\theta \,\!](/Images/godic/202501/27/0a5000fe8b6b5570dd5a1ce00b828ef62751.png")
. In a sense this means that is an estimator which performs best in the worst possible case allowed in the problem.