One-step smoothing splines instrumental regression
将非参数回归平滑样条扩展到存在内生性和工具变量的情境，提出一步估计法，仅依赖一个正则化参数，并证明估计量及其一阶导数的收敛速度，模拟显示优于两步法，应用于恩格尔曲线估计得到合理结果。
Summary We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one step and relies on a unique regularisation parameter. We derive rates of the convergence for the estimator and its first derivative, which are uniform in the support of the endogenous variable. We also address the issue of imposing monotonicity in estimation and extend the approach to a partly linear model. Simulations confirm the good performances of our estimator compared to two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.