Ordered inference using observed confidence levels

Statistical inference on the ordering of the elements of a mean vector is an important issue in many applied problems, particularly in biostatistical applications. Some common ordering models include simple, tree and umbrella orderings. Many statistical methods have been developed to detect these orderings within the normal model, and outside the normal model using nonparametric methods. Estimates as well as confidence regions have also been developed for the mean vector under constraints imposed by these ordering models. In order to attempt to distinguish between ordered models, multiple testing procedures are usually required to control the overall error rate of the sequence of tests. This paper shows how observed confidence levels allow for the exploration of very general ordering models without the need for specialized asymptotic theory or multiple testing methods. The proposed methods are applied to several examples.