Functional relative error regression under left truncation and right censoring

The nonparametric estimators built by minimizing the mean squared relative error are gaining in popularity for their robustness in the presence of outliers in comparison to the Nadaraya Watson estimators. In this paper we build a relative error regression function estimator in the case of a functional explanatory variable and a left truncated and right censored scalar variable. The pointwise and uniform convergence of the estimator is proved and its performance is assessed by a numerical study in particularly the robustness which is highlighted using the influence function as a measure of robustness.