For the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the regression functions. By applying the conditional expectation directly to the kernel-weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function, if the bandwidth is less than the SD of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications.

中文翻译：

---

具有测量误差的非参数回归的外推估计

针对协变量受到正态测量误差污染的非参数回归模型，本文提出了一种外推算法来估计回归函数。通过将条件期望直接应用于局部线性近似与观测响应之间偏差的核加权最小二乘，所提出的算法成功地绕过了经典模拟外推中的模拟步骤，从而显着减少了计算时间。值得注意的是，所提出的方法还提供了外推函数的精确形式，尽管如果带宽小于测量误差。讨论了所提出的估计程序的大样本属性，并进行了模拟研究和真实数据示例来说明其应用。