Test d'hétéroscédasticité quand les covariables sont fonctionnelles

We present in this paper a consistent nonparametric test for heteroscedasticity when data are of functional kind. The latter is constructed by evaluating the difference between the conditional and unconditional variances. We show the asymptotic normality of the statistical test under the null hypothesis. In addition, we prove that this test is consistent against all deviations from homoscedasticity condition.