This paper considers a new estimating method for the bent line quantile regression model. By a simple linearization technique, the proposed method can simultaneously obtain the estimates of the regression coefficients and the change-point location. Moreover, it can be readily implemented by current software. Simulation studies demonstrate that the proposed method has good finite sample performance. Two empirical applications are also presented to illustrate the method.
Predicting and allocating water resources have become important tasks in water resource management. System dynamics and optimal planning models are widely applied to solve individual problems, but are seldom combined in studies. In this work, we developed a framework involving a system dynamics-multiple objective optimization (SD-MOO) model, which integrated the functions of simulation, policy control, and water allocation, and applied it to a case study of water management in Jiaxing, China to demonstrate the modeling. The predicted results of the case study showed that water shortage would not occur at a high-inflow level during 2018–2035 but would appear at mid- and low-inflow levels in 2025 and 2022, respectively. After we made dynamic adjustments to water use efficiency, economic growth, population growth, and water resource utilization, the predicted water shortage rates decreased by approximately 69–70% at the mid- and low-inflow levels in 2025 and 2035 compared to the scenarios without any adjustment strategies. Water allocation schemes obtained from the "prediction + dynamic regulation + optimization" framework were competitive in terms of social, economic and environmental benefits and flexibly satisfied the water demands. The case study demonstrated that the SD-MOO model framework could be an effective tool in achieving sustainable water resource management.
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
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