Nonparametric tests of hypotheses for umbrella alternatives

Abstract

A general method for nonparametric hypothesis testing for umbrella alternatives is proposed. Such alternatives arise in situations where the treatment effect changes in direction after reaching a peak. The approach consists of defining two sets of rankings, one corresponding to the observations and the other to the alternative. The test statistic measures the distance between the two sets. The limiting distributions are obtained under the null hypothesis when the location of the peak is known. The simulation study shows good power of the test. A method is proposed for estimating the location of the peak, if it is unknown.