In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.

中文翻译：

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拉普拉斯测量误差存在下的模态非线性回归

在本文中，当协变量被拉普拉斯测量误差污染时，我们为一类非线性回归模型提出了一种鲁棒的估计程序，旨在为回归参数构造一个估计程序，该估计程序不受可能的异常值的影响，而且较重尾部的基础分布，以及减少测量误差引起的偏差。从针对无测量误差情况开发的模态回归程序开始，进行了不小的修改，以便修改后的版本可以有效地校正由测量误差引起的潜在偏差。对提议的估计的大样本属性（例如收敛速度和渐近正态性）进行了彻底研究。