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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (3): 69-76.doi: 10.6040/j.issn.1671-9352.0.2024.084

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基于线性化技术的变点分位数回归模型的估计与应用

周小英1,2,吉晨1,涂晓艺1*   

  1. 1.海南师范大学数学与统计学院, 海南 海口 571158;2.海南师范大学数据科学与智慧教育教育部重点实验室, 海南 海口 571158
  • 发布日期:2025-03-10
  • 通讯作者: 涂晓艺(2000— ),女,硕士研究生,研究方向为应用统计. E-mail:txy18181281029@163.com
  • 作者简介:周小英(1989— ),女,副教授,博士,研究方向为变点数据建模与应用. E-mail:zhouxy213@163.com*通信作者:涂晓艺(2000— ),女,硕士研究生,研究方向为应用统计. E-mail:txy18181281029@163.com
  • 基金资助:
    国家自然科学地区基金资助项目(72263007);2023年海南省研究生创新科研课题项目(Qhys2023-384)

Estimation and application of the change-point quantile regression model based on linearization technique

ZHOU Xiaoying1,2, JI Chen1, TU Xiaoyi1*   

  1. 1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, Hainan, China;
    2. Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, Hainan, China
  • Published:2025-03-10

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摘要： 构建变点分位数回归模型,该模型由1条直线和1条二次曲线在变点处相交而成,可以灵活处理变点数据,还能捕捉响应变量分布的全貌。由于变点参数的存在,使得模型的损失函数是非凸的,给估计参数带来了挑战。为了解决这个问题,基于线性化技术将损失函数线性化,利用迭代算法,同时得到变点参数和其他参数的估计,给出估计量的区间估计。数值模拟结果表明,本文的估计方法具有良好的相合性和有效性,人均国内生产总值与电力质量数据的实证分析也验证了所提模型和方法的可行性和实用性。

关键词: 变点, 线性-二次分位数回归模型, 线性化技术, 电力质量

Abstract: The change-point quantile regression model constructed by the intersection of a straight line and a quadratic curve at a change point. This model can flexibly handle change point data and capture the overall distribution of the response variable. Due to the presence of the change point parameter, the models loss function is non-convex, which is a challenge for parameter estimation. To address this issue, the loss function is linearized based on the linearization technique combining with an iterative algorithm, which can simultaneously estimate the change point and other parameters. The interval estimation theory for the estimators is also derived. Numerical simulation results indicate that the proposed estimation method exhibits good consistency and effectiveness. Empirical analysis of per capita GDP and power quality data further verifies the feasibility and practicality of the proposed model and method.

Key words: change point, linear quadratic quantile regression model, linearization technique, power quality

中图分类号: 

  • O213.9
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