Optimal smoothing parameter selection in single-index model derivative estimation
针对单指数模型导数估计中的平滑参数选择问题，提出一种数据驱动的最优选择方法，并推导了局部线性估计量的渐近分布，模拟和实证表明方法有效。
.Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying “marginal effects” serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (Citation2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the “curse of diemnsionality” problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (Citation2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice.