Admissible decision rule

A Decision rule $\delta$ is inadmissible if there exists a $\delta^* \in \mathcal{D}$ such that $R(\theta, \theta^*) \leq R(\theta, \delta)$ where the inequality is strict for some $\delta \in \Theta$; otherwise $\delta$ is admissible.

Here $R$ is the Risk function, $\mathcal{D}$ is the space of possible decision rules, and $\Theta$ is the space of possibilities which we consider (for instance, Parameters in the case of Parametric statistical inference).

See minimax_and_bayes_estimator.pdf for explanation of the decision-theoretic formalism used here

related to Pareto optimality

Let T be the unique Bayes estimator of θ with respect to the prior density π. Then T is admissible.