An essential assumption in traditional regression techniques is that predictors are measured without errors. Failing to take into account measurement error in predictors may result in severely biased inferences. Correcting measurement-error bias is an extremely difficult problem when estimating a regression function nonparametrically. We propose an approach to deal with measurement errors in predictors when modelling flexible regression functions. This approach depends on directly modelling the mean and the variance of the response variable after integrating out the true unobserved predictors in a penalized splines model. We demonstrate through simulation studies that our approach provides satisfactory prediction accuracy largely outperforming previously suggested local polynomial estimators even when the model is incorrectly specified and is competitive with the Bayesian estimator.

传统回归技术中的一个基本假设是，预测变量的测量没有错误。如果不考虑预测变量中的测量误差，可能会导致推论的严重偏差。当非参数地估计回归函数时，校正测量误差偏差是一个极其困难的问题。我们提出了一种在对灵活的回归函数进行建模时处理预测变量中的测量误差的方法。这种方法依赖于在惩罚样条曲线模型中整合出真正的未观察到的预测因子后，直接对响应变量的均值和方差建模。