This paper is concerned with a nonparametric estimator of the regression function based on the local linear method when the loss function is the mean squared relative error and the data left truncated. The proposed method avoids the problem of boundary effects and is robust against the presence of outliers. Under suitable assumptions, we establish the uniform almost sure strong consistency with a rate over a compact set. A simulation study is conducted to comfort our theoretical result. This is made according to different cases, sample sizes, rates of truncation, in presence of outliers and a comparison study is made with respect to classical, local linear and relative error estimators. Finally, an experimental prediction is given.

本文关注的是当损失函数为均方相对误差且数据被截断时，基于局部线性方法的回归函数的非参数估计量。所提出的方法避免了边界效应的问题，并且对异常值的存在具有鲁棒性。在适当的假设下，我们在一个紧集上建立了具有速率的一致几乎肯定的强一致性。进行模拟研究以安慰我们的理论结果。这是根据不同的情况、样本量、截断率、存在异常值的情况进行的，并针对经典、局部线性和相对误差估计量进行比较研究。最后给出了实验预测。