Single-index Thresholding in Quantile Regression

Threshold regression models are useful for identifying subgroups with heterogeneous parameters. The conventional threshold split the sample based on a single and observed variable, which enforces point to be equal all of population. In this article, we consider more flexible single-index model in quantile setup, is linear combination predictors. We propose new estimator by smoothing indicator function thresholding, enables Gaussian approximation statistical inference allows characterizing limiting distribution when process interested. further construct mixed-bootstrap method faster computation procedure testing constancy parameters across quantiles. Finally, demonstrate value proposed methods via simulation studies, as well through application an executive compensation data.