We investigate the errors in covariates issues in a generalized partially linear model. Different from the usual literature (Ma and Carroll in J Am Stat Assoc 101:1465–1474, 2006), we consider the case where the measurement error occurs to the covariate that enters the model nonparametrically, while the covariates precisely observed enter the model parametrically. To avoid the deconvolution type operations, which can suffer from very low convergence rate, we use the B-splines representation to approximate the nonparametric function and convert the problem into a parametric form for operational purpose. We then use a parametric working model to replace the distribution of the unobservable variable, and devise an estimating equation to estimate both the model parameters and the functional dependence of the response on the latent variable. The estimation procedure is devised under the functional model framework without assuming any distribution structure of the latent variable. We further derive theories on the large sample properties of our estimator. Numerical simulation studies are carried out to evaluate the finite sample performance, and the practical performance of the method is illustrated through a data example.

中文翻译：

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具有非线性函数测量误差的广义部分线性模型的局部有效估计。

我们调查广义部分线性模型中协变量问题中的错误。与通常的文献不同（Ma和Carroll在J Am Stat Assoc 101：1465-1474，2006）中，我们考虑了以下情况：测量误差发生于非参数进入模型的协变量，而精确观察到的协变量则以参数进入模型。为了避免反卷积类型的运算（可能会产生非常低的收敛速度），我们使用B样条表示法来近似非参数函数，并将问题转换为参数形式以用于运算目的。然后，我们使用参数化工作模型来替换不可观察变量的分布，并设计一个估计方程来估计模型参数和对潜在变量的响应的函数依赖性。估计程序是在功能模型框架下设计的，没有假定潜在变量的任何分布结构。我们进一步推导有关估计量的大样本属性的理论。进行了数值模拟研究，以评估有限样品的性能，并通过一个数据示例说明了该方法的实际性能。