Testing problems with linear or angular inequality constraints

The present study is concerned mainly with certain generalizations of one-sided hypothesis testing problems, namely problems where the alternative is restricted by at least two linear inequalities. A celebrated example in the statistical literature is that of testing homogeneity against upward trend, say in the context of a one-way analysis of variance. A secondary theme of the present study is constituted by testing problems where linear inequalities restrict the null hypothesis rather than the alternative (but not both). An example arises if the model assumption of upward trend has to be tested against the alternative that at least two samples violate the assumed order of treatment means. ... Zie: General introductlon and summary