Due to the fast growth of data that are measured on a continuous scale, functional data analysis has undergone manydevelopments in recent years. Regression models with a functional response involving functional covariates, also called“function-on-function”, are thus becoming very common. Studying this type of model in the presence of heterogeneous datacan be particularly useful in various practical situations. We mainly develop in this work a function-on-function Mixtureof Experts (FFMoE) regression model. Like most of the inference approach for models on functional data, we use basisexpansion (B-splines) both for covariates and parameters. A regularized inference approach is also proposed, it accuratelysmoothes functional parameters in order to provide interpretable estimators. Numerical studies on simulated data illustratethe good performance of FFMoE as compared with competitors. Usefullness of the proposed model is illustrated on two datasets: the reference Canadian weather data set, in which the precipitations are modeled according to the temperature, and aCycling data set, in which the developed power is explained by the speed, the cyclist heart rate and the slope of the road.

https://indico.math.cnrs.fr/event/13013/