Nonparametric modeling via two-way mixed effects design

The classical F-test for testing the hypothesis of no fixed main effects in a mixed effects design is valid under the assumption of normality, symmetry and variance homogeneity of the error terms assumption. We consider the two-way mixed effects design which does not require these three assumptions. A test procedure for the hypothesis of no main fixed effects is developed under this flexible model. The asymptotic distribution of the test statistic is studied for a large number of levels of the random effects.