Nonparametric relative error regression for functional time series data under random censorship

In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a dependent functional explanatory variable, in the case of a scalar censored response. We use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional censored data. We establish the almost surely convergence (with rates) and the asymptotic normality of the proposed estimator. A simulation study and real data application are performed to lend further support to our theoretical results and to compare the quality of predictive performances of the relative error regression estimator than those obtained with standard kernel regression estimates.