Towards a Calculus for Admissibility

Abstract

It is shown how the calculus can be used to characterize admissible decision rules (Pareto optimal points, efficient points). Necessary and sufficient conditions for admissibility are derived in terms of the first and the second directional derivatives of convex risk functions. In particular, the results obtained imply that if $p$ is to be estimated in the binomial distribution $B(n, p)$, then an estimator is admissible for the quadratic loss function if and only if it fulfills some analytic conditions.