带多个变点的逐段连续线性分位数回归模型及应用

A Continuous Piecewise Linear Quantile Regression with Multiple Change-points

研究目标:建立具有多个变点的逐段连续线性分位数回归模型(Continuous Piecewise Linear Quantile Regression with Multiple Change Points,CPLQR)。研究方法:先通过LASSO和广义贝叶斯信息准则确定变点个数,再通过线性化技巧来估计变点的位置与回归系数。研究发现:新方法能够同时确定变点个数、估计变点位置和回归系数,而且具有较强的稳健性;应用该方法于年龄和身体质量指数之间关系,进一步证实了模型的实用性。研究创新:新方法能够处理多个变点的问题,通过LASSO和广义贝叶斯信息准则确定变点数目,避免了主观判断的弊端;借助线性化技巧,解决了目标函数在变点处不可导问题。研究价值:本文结果将为分析经济、金融、医药和生物等学科中存在结构变化的数据提供强有力的研究工具。

Research Objectives： To propose a new method for a continuous piecewise linear quantile regression model with multiple change points （CPLQR）. Research Methods： Estimating pro- cedure determines the number of change-points by LASSO and generalized BIC, and then the locations of change-points and regression coefficients are estimated by a linearization tech- nique. Research Findings： The new method can not only determine the number of change- points, but also simultaneously and robustly estimate the locations of change-points and the regression coefficients. We apply the new method to analyze the relationship between the age and the BMI, which demonstrates the practical utility of the methodology. Research Innova- tions： The new method could deal with multiple change points problem, and the number of change points is determined by Lasso and generalized BIC. By utilizing a linearization tech- nique, the new method overcomes the non-differentiability of the objective function due to the existence of change points. Research Value： This paper provides an effective tool for the data with change points in various research areas, such as economics, finance, biology, med- icine and so on.