“…Our proposal shares this problem with other one‐sided test versions such as the ALR test of Tang et al. (
1993), one‐sided applications of O'Brien's (
1984) test versions or the proposal of Glimm and Läuter (
2010). Even in a multiple test procedure with local tests for each component of
, it would be difficult to achieve a strict type I error control over the whole parameter space outside the positive orthant without dramatic power losses in situations where group differences in the desired direction occur only in some of the variables.…”