Minimax
Minimax criterion in statistical decision theory

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

An alternative criterion in the decision theoretic framework is the Bayes estimator in the presence of a prior distribution Π. {\displaystyle \Pi \.} An estimator is Bayes if it minimizes the average risk
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