Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian nonparametric regression. This problem becomes tremendously more difficult when considering other families such as logistic regression, Poisson and negative-binomial. For the first time, we present a method aiming to correct for measurement error when estimating regression functions flexibly covering virtually all distributions and link functions regularly considered in generalized linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in a semiparametric generalized linear model. Unlike previous methods, this method is not restricted to truncated splines and can utilize various basis functions. Through extensive simulation studies, we study the performance of our method under many scenarios.

翻译：忽略预测变量测量误差的回归模型可能会产生高度有偏的估计，从而导致错误的推断。众所周知，在高斯非参数回归中考虑测量误差极为困难。当考虑逻辑回归、泊松回归和负二项回归等其他族时，这一问题变得更加棘手。我们首次提出了一种方法，旨在灵活估计涵盖广义线性模型中几乎所有常见分布和链接函数的回归函数时，对测量误差进行校正。该方法依赖于在半参数广义线性模型中，对真实未观测预测变量进行积分后，对响应变量的第一矩和第二矩进行近似。与以往方法不同，本方法不局限于截断样条，而是可以利用多种基函数。通过广泛的模拟研究，我们在多种场景下考察了所提方法的性能。