Minimax

Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. It started from two player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves. It has also been extended to more complex games and to general decision making in the presence of uncertainty.

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In classical statistical decision theory, we have an estimator delta that is used to estimate a parameter heta in Theta. We also assume a risk function R( heta,delta), usually specified as the integral of a loss function. In this framework, ilde{delta} is called minimax if it satisfies

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: sup_ heta R( heta, ilde{delta}) = inf_delta sup_ heta R( heta,delta).

Decision theory: Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. It is concerned with how real decision-makers make decisions, and with how optimal decisions can be reached....

Loss: Loss has several meanings including:...

Zero-sum: Zero-sum describes a situation in which a participant's gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). It is so named because when you add up the total gains of the participants and subtract the total losses then they will sum to zero. Cutting a cake is zer...