For the nonparametric regression models with covariates contaminated with normal measurement errors, this paper proposes an extrapolation algorithm to estimate the nonparametric 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 needed in the classical simulation extrapolation method, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, but 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 standard deviation 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.

翻译：对于具有受正常测量误差污染的共差的非参数回归模型,本文件建议采用一种外推算法来估计非参数回归函数。如果带宽低于测量误差的标准偏差,则将有条件的预期直接应用到本地线性近似值和观察到的响应之间的偏差内核加权最小方形,拟议算法成功地绕过了经典模拟外推法所需的模拟步骤,从而大大减少了计算时间。有人指出,拟议方法也提供了外推函数的准确形式,但通常无法通过在安装的外推函数中将外推变量设为负值来获得外推法估计。会议讨论了拟议估算程序的大量抽样特性,以及模拟研究和为说明其应用而正在进行的实际数据实例。