## The Annals of Statistics

### Towards a Calculus for Admissibility

Andrzej Kozek

#### 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.

#### Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 825-837.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345874

Digital Object Identifier
doi:10.1214/aos/1176345874

Mathematical Reviews number (MathSciNet)
MR663435

Zentralblatt MATH identifier
0498.62010

JSTOR