The problem of multiple endpoint testing for k endpoints is treated as a 2 finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), th...

This work includes a new characterization of the multivariate normal distribution. In particular, it is shown that positive density function f Gaussian if and only ( x + y ) / convex in for every . result has implications to recent research regarding inadmissibility test studied by Moran (1973).