In many situations, the random variables take values in a Riemannian manifold $(M, g)$ instead of $\mathbb{R}^d$, and this structure needs to be taken into account when we generate estimation procedures. For the nonparametric regression model, we study two families of robust estimators for the regression function when the explanatory variables take values in a Riemannian manifold.

In this talk, we will give a brief introduction of the geometric objects needed to define the nonparametric estimators adapted to a manifold. We discuss the classical proposals and we introduce two families of robust estimators for the regression function. We show the asymptotic properties obtained for both proposal. Finally, through a simulation study, we compare the behavior of the robust estimators against the alternative classic. This is a joint work with Guillermo Henry.