A Study on the Nonparametric Simultaneous Tests for the Location and Scale Parameters

In this research, we consider a nonparametric simultaneous test procedure for the location and scale parameters. For this, first of all, we formulate the null hypothesis and its alternative under the location-scale model. Then we propose three types of nonparametric tests with the three different combining functions to combine the results of the individual tests based on the well-known nonparametric tests for each parameter. We use the p-values for the results of the individual tests. Then we compare two procedures for the efficiency by obtaining the empirical powers for the five different underlying distributions through a simulation study. One procedure uses the Mood test and the other is the Ansari-Bradley one for the scale parameter. Then we discuss some interesting aspects related to the simultaneous tests with the types of alternatives which can be adopted to our procedure and obtaining the p-values for each individual test. Finally we comment briefly the use of bootstrap method in our procedure.