Adaptive tests for umbrella alternatives

Recently, BONING and KOSSLER (1997) studied so called Mack-Wolfe-type tests in which the Mann-Whitney statistics, used by MACK and WOLFE (1981), are replaced by other two-sample linear rank statistics. Each of the Mack-Wolfe-type tests considered has high power for a special distribution. In practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes into account the given data set. Two versions of such an adaptive test based on the concept of HOGG (1974) are proposed and compared with the four Mack-Wolfe-type tests in the adaptive scheme. The power comparison is carried out via Monte Carlo simulation and takes into consideration the case of estimating the unknown peak. It is shown that the adaptive tests behave well over a broad class of symmetric and asymmetric distributions.