A logarithmic calibration estimation procedure is proposed for nonparametric regression models under the multiplicative distortion measurement errors setting. The unobservable response variable and covariates are both distorted in a multiplicative fashion by an observed confounding variable. By using the logarithmic calibration estimation procedure for unobserved variables, we consider to study the estimates of nonparametric mean function and its first derivative, the variance function, the Sharpe ratio function and correlation curve. We obtain asymptotic normality results for the proposed nonparametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyse a real dataset for an illustration.

针对乘法失真测量误差设置下的非参数回归模型提出了对数校准估计程序。不可观察的响应变量和协变量都被观察到的混杂变量以乘法方式扭曲。通过对未观测变量使用对数校准估计程序，我们考虑研究非参数均值函数及其一阶导数、方差函数、夏普比率函数和相关曲线的估计。我们获得了所提出的非参数估计量的渐近正态性结果。进行蒙特卡罗模拟实验以检查所提出的估计器的性能。建议的估计器用于分析真实数据集以进行说明。