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.
Publication:
Journal of the American Statistical Association. Available online 01 Jun 2021
Author:
Yingying Zhang,
Academy of Statistics and Interdisciplinary Sciences, KLATASDS-MOE,
East China Normal University, Shanghai, China
Huixia Judy Wang,
Department of Statistics, The George Washington University, Washington, DC
Email: judywang@gwu.edu
Zhongyi Zhu,
Department of Statistics, Fudan University, Shanghai, China