Bent line quantile regression via a smoothing technique

Abstract

A bent line quantile regression model can describe the conditional quantile function of the response variable with two different straight lines, which intersect at an unknown change point. This paper proposes a new approach via a smoothing technique to simultaneously estimate the location of the change point and other regression coefficients for the bent line quantile regression model. Furthermore, the asymptotic properties of the proposed estimator are derived, and a formal test procedure for the existence of a change point is also provided. Simulation studies are carried out to demonstrate the finite sample performance of the proposed method. We also illustrate the proposed method by applying it to the gross domestic product (GDP) per capita and the life expectancy at birth data. K E Y W O R D S change point, quantile regression, smoothing technique

Estimation and inference for multikink expectile regression with longitudinal data

“…Unfortunately, the loss function of the QR is not differentiable at some parameter points, which makes its computation difficult and is hard to derive high-order statistical properties. To solve this problem, Yan et al 20 and Zhou and Zhang 21 applied the linearization technique and kernel smoothing for the bent line QR, respectively. Recently, Zhong et al 22 considered the estimation and inference for multiple kink QR models.…”