线性回归模型多变点的LAD-LASSO估计  

LAD-LASSO estimation of multiple change points in linear regression model

作　　者：王珊 赵文芝[1] WANG Shan;ZHAO Wenzhi(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《西安工程大学学报》2023年第2期113-118,共6页Journal of Xi’an Polytechnic University

基　　金：国家自然科学基金面上项目(12171391);陕西省自然科学基础研究计划项目(2022JM-024)。

摘　　要：将最小绝对偏差(least absolute deviations,LAD)和最小绝对收缩与选择算子(least absolute shrinkage with selection operator,LASSO)相结合,研究线性回归模型多变点的估计问题,即LAD-LASSO估计。将多变点估计转化为变量选择问题,通过最小化目标函数得到变点位置及变点个数的LAD-LASSO估计。模拟比较LAD-LASSO方法与传统的LASSO方法,结果显示LAD-LASSO方法得到的变点估计值集合与真实值集合之间的Hausdorff距离更小,表明LAD-LASSO方法具有更好的稳健性。估计上海机场股票(600009)收益率数据的方差变点,验证了方法的有效性。Combining least absolute deviation(LAD)and least absolute shrinkage with selection operator(LASSO),we studied the multiple change points estimation problem in linear regression models,that is,the LAD-LASSO estimation.Firstly,the multiple change points estimation problem was transformed into a variable selection problem.Secondly,the locations and number of change points were estimated by minimizing the objective function.Thirdly,the simulation study was carried out between the LAD-LASSO method and the traditional LASSO method.Simulation results show that the Hausdorff distance between the change points estimation set and the true value set obtained by the LAD-LASSO is smaller than that of LASSO,which indicates that the LAD-LASSO method has better robustness.Finally,we estimated the variance change points of Shanghai airport stock(600009)yield data,and the results show that the proposed method can be used to deal with practical problems.

关 键 词：线性回归 多变点 LAD-LASSO HAUSDORFF距离 

分 类 号：O212.1[理学—概率论与数理统计]