In this paper a Canonical Correlation Analysis (CCA) is used to test the hypothesis r = r0 against the alternative r r0. Such a test flips the null and alternative hypotheses of Johansen's LR test and can be used jointly with the LR test to construct a confidence set for the cointegration rank....

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...

Bayesian decisions are observationally identical to decisions with judgment. Decisions with judgment test whether a judgmental decision is optimal and, in case of rejection, move to the closest boundary of the confidence interval, for a given confidence level. The resulting decisions condition...