Smoothed gradient least squares estimator for linear threshold models
针对固定阈值效应下最小二乘估计量极限分布非标准的问题，提出两步平滑梯度最小二乘估计量，实现阈值参数的正态极限分布，并通过改进的bootstrap方法提高计算效率和置信区间精度。
In the presence of fixed threshold effects, the least squares (LS) estimator of the threshold parameter poses challenges for statistical inference due to its nonstandard limiting distribution, which also presents challenges for bootstrap methods. To address this issue, we propose a novel estimator: a two-step smoothed gradient least squares (SGLS) estimator. Our proposed method achieves a normal limiting distribution for the threshold parameter with minimal efficiency loss compared to the LS estimator. Furthermore, our modified bootstrap method significantly enhances computational efficiency, leading to improved bootstrap confidence intervals (CIs) for the threshold parameter compared to asymptotic CIs. Our method is validated through a small Monte Carlo study and demonstrated with an empirical application.