Adaptive Jonckheere-type tests for ordered alternatives

Abstract

Testing against ordered alternatives in the c -sample location problem plays an important role in statistical practice. The parametric test proposed by Barlow et al .-in the following, called the 'B-test'-is an appropriate test under the model of normality. For non-normal data, however, there are rank tests which have higher power than the B-test, such as the Jonckheere test or so-called Jonckheere-type tests introduced and studied by Buning and Kossler. However, we usually have no information about the underlying distribution. Thus, an adaptive test should be applied which takes into account the given data set. Two versions of such an adaptive test are proposed, which are based on the concept introduced by Hogg in 1974. These adaptive tests are compared with each of the single Jonckheere-type tests in the adaptive scheme and also with the B-test. It is shown via Monte Carlo simulation that the adaptive tests behave well over a broad class of symmetric distributions with short, medium and long tails, as well as for asymmetric distributions.