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.

翻译：基于最小化均方相对误差构建的非参数估计量，因其相比Nadaraya-Watson估计量在异常值存在时具有更强稳健性而日益受到关注。本文针对函数型解释变量与左删失右截尾标量响应变量的情形，构建了相对误差回归函数的估计量。证明了该估计量的逐点收敛性与一致收敛性，并通过数值研究评估其性能，特别利用影响函数作为稳健性度量突出了其稳健性特征。