  A new nonparametric graphical test of significance of a covariate in
functional GLM is proposed. Our approach is especially interesting due to its
functional graphical interpretation of the results. As such it is able to find
not only if the factor of interest is significant but also which functional
domain is responsible for the potential rejection. In the case of functional
multi-way main effect ANOVA or functional main effect ANCOVA models it is able
to find which groups differ (and where they differ), in the case of functional
factorial ANOVA or functional factorial ANCOVA models it is able to find which
combination of levels (which interactions) differ (and where they differ). The
described tests are extensions of global envelope tests in the GLM models. It
applies Freedman-Lane algorithm for the permutation of functions and as such it
approximately achieve the desired significance level.
