Admissibility of invariant procedures. If a decision problem remains invariant under a finite group, and if there exists a procedure δ0 that uniformly minimizes the risk among all invariant procedures, then δ0 is admissible.

[This follows from the identity R(θ, δ) = R(g¯θ, g∗δg−1) and the hint given in Problem 1.11(i).]