Estimation in quantile regression models with jump discontinuities

Abstract

In quantile regression, the quantile function is often discontinuous so that it is needful to detect the jump points. In the existing literature, it is generally assumed the jump number to be known. In most applications, however, it is not uncommon that the jump number is often unknown so that the existing methods of detecting jump discontinuities are no longer applicable. In this paper, we first propose a new procedure of detecting jump by using the local polynomial techniques for the case of the unknown jump number. We then propose the estimators of jump points, jump sizes and jump number, and study their asymptotic properties. Finally, we conduct simulation studies to assess the finite sample performance of our proposed estimators and present their biases and standard errors to demonstrate that our proposed method performs well in a wide range of practical settings.

Keywords:

• Jump point
• jump size
• local polynomial regression
• quantile regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F12

Additional information

Funding

Yuejin Zhou’s research was supported in part by the Ph.D. Programs Foundation of Anhui University of Science and Technology (No.ZY514) and the National Natural Science Foundation of China grant (No. 61703005). Chi Ma’s research was supported in part by the National Natural Science Foundation Pre-research grant of Anhui University of Science and Technology (No.YY201804). Dequan Li’s research was supported in part by the National Natural Science Foundation of China grant (No. 61472003).