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.
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