Single-index Thresholding in Quantile Regression
本文在分位数回归框架下提出一种更灵活的单指标阈值模型，通过平滑指示函数估计阈值，并构建混合自助推断方法，用于分析高管薪酬数据。
Threshold regression models are useful for identifying subgroups with heterogeneous parameters. The conventional threshold regression models split the sample based on a single and observed threshold variable, which enforces the threshold point to be equal for all subgroups of the population. In this article, we consider a more flexible single-index threshold model in the quantile regression setup, in which the sample is split based on a linear combination of predictors. We propose a new estimator by smoothing the indicator function in thresholding, which enables Gaussian approximation for statistical inference and allows characterizing the limiting distribution when the quantile process is interested. We further construct a mixed-bootstrap inference method with faster computation and a procedure for testing the constancy of the threshold parameters across quantiles. Finally, we demonstrate the value of the proposed methods via simulation studies, as well as through the application to an executive compensation data.