Strong convergence of the functional nonparametric relative error regression estimator under right censoring

Abstract

Abstract In this paper, we investigate the asymptotic properties of a nonparametric estimator of the relative error regression given a 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 strong almost complete convergence rate and asymptotic normality of these estimators. A simulation study is performed to illustrate and compare the higher predictive performances of our proposed method to those obtained with standard estimators.