Statistical Decision Functions with Judgment

Abstract

A decision maker tests whether the gradient of the loss function evaluated at a judgmental decision is zero. If the test does not reject, the action is the judgmental decision. If the test rejects, the action sets the gradient equal to the boundary of the rejection region. This statistical decision rule is admissible and conditions on the sample realization. The confidence level reflects the decision maker’s aversion to statistical uncertainty. The decision rule is applied to a problem of asset allocation.