# A nonparametric graphical tests of significance in functional GLM

## TL;DR

This paper introduces a nonparametric graphical testing method for functional GLMs that visually identifies significant covariate effects and their specific functional domains, enhancing interpretability in complex models.

## Contribution

It presents a novel graphical significance test for functional GLMs that reveals where and how factors influence the functional response, extending global envelope tests with permutation-based significance control.

## Key findings

- Effective identification of significant covariate effects in functional data.
- Ability to pinpoint specific functional domains responsible for significance.
- Extension of global envelope tests to functional GLMs.

## Abstract

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.