We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of this semiparametric model. We then show the asymptotic normality of the parametric estimator and obtain the convergence rate for the nonparametric estimator. Our estimator that does not smooth on the instruments coincides with a typical estimator that does smooth on the instruments but keeps the respective bandwidth fixed as the sample size increases. We propose a data driven method for the selection of the regularization parameter, and in a simulation study we show the attractive performance of our estimators.

翻译：我们考虑一类由工具变量识别的半参数部分线性模型。本文提出一种无需对工具变量进行平滑处理的估计方法，并将Landweber-Fridman正则化方案扩展至该半参数模型的估计。我们随后证明了参数估计量的渐近正态性，并获得了非参数估计量的收敛速度。这种不对工具变量进行平滑的估计量与典型的需要平滑工具变量的估计量在保持各自带宽随样本量增大而固定时具有一致性。我们提出了一种数据驱动的正则化参数选择方法，并通过模拟研究展示了所提估计量的优良表现。