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.

中文翻译：

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通过平滑技术进行折线分位数回归

折线分位数回归模型可以用两条不同的直线描述响应变量的条件分位数函数，两条直线在一个未知的变化点处相交。本文提出了一种通过平滑技术同时估计折线分位数回归模型的变化点位置和其他回归系数的新方法。此外，推导了所提出估计量的渐近性质，并且还提供了用于存在变化点的形式化测试程序。仿真研究表明了该方法的有限样本性能。我们还通过将其应用于人均国内生产总值（GDP）和出生时预期寿命数据来说明该方法。