Non parametric multiple comparisons of non nested rival models

The practice for testing homogeneity of several rival models is of interest. In this article, we consider a non parametric multiple test for non nested distributions in the context of the model selection. Based on the linear sign rank test, and the known union–intersection principle, we let the magnitude of the data to give a better performance to the test statistic. We consider the sample and the non nested rival models as blocks and treatments, respectively, and introduce the extended Friedman test version to compare with the results of the test based on the linear sign rank test. A real dataset based on the waiting time to earthquake is considered to illustrate the results.