Introduction and Notation

Abstract

This work presents a method of using projections of functions onto convex cones in Hilbert spaces for determining sharp bounds on values of statistical functionals over general and restricted families of distributions, expressed in terms of moment parameters of the distributions. The method is based on representing the statistical functionals and families of distributions as fixed elements and convex cones, respectively, in a common real Hilbert space. Then the norm of the projection of the element onto the cone provides the optimal bound. The distribution for which the bound is attained is derived by a simple transformation of the projection.