Adaptive tests for trend

In the nonparametric location model the Jonckheere (1954) trend test is powerful for convex shapes of the location parameters, whereas the Fligner and Wolfe (1982) test is powerful for concave shapes. Since in most situations knowledge about the shape is a priori lacking, we suggest an adaptive test which classifies the shape. We use the skewness of the pooled sample as a selector statistic. An adaptive trend test which classifies the shape is also possible in the parametric model where we consider contrast tests. In both models the adaptive trend test is - analogous to other adaptive tests - not optimal for any particular shape but relatively good over all shapes.