Robust equivariant non parametric regression estimators for functional ergodic data

This article deals with the equivariant non parametric robust regression estimation for stationary ergodic processes valued in where is a semi-metric space. We consider a new robust regression estimator when the scale parameter is unknown. The principal aim is to prove the almost complete convergence (with rate) for the proposed estimator. Unlike in standard multivariate cases, the gap between pointwise and uniform results is not immediate. So, suitable topological considerations are needed, implying changes in the rates of convergence which are quantified by entropy considerations.