线性回归模型中相依数据的多结构变点的估计  

Multiple structural break estimations for linear regression with dependent observations

作　　者：李美琪 金百锁[1] 董翠玲[2] Meiqi Li;Baisuo Jin;Cuiling Dong

机构地区：[1]中国科学技术大学管理学院,合肥230026 [2]新疆师范大学数学科学学院,乌鲁木齐830017

出　　处：《中国科学：数学》2023年第7期1007-1024,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:71873128,72111530199和11801488);安徽省自然科学基金(批准号:2108085J02)资助项目。

摘　　要：多变点线性模型经常应用于统计学和计量经济学中.本文通过分割数据并建立相依观测数据的高维线性回归模型,将变点检测问题转化为变量选择问题.在变量选择中,应用组正交贪婪算法(group orthogonal greedy algorithm,GOGA)来解决变点数量随观测数量的增加而增加的情形,并结合高维信息准则(high-dimensional information criteria,HDIC)以防止过度拟合.第一阶段采用GOGA+HDIC+Trim对分段数据进行变量选择来降低计算成本,第二阶段应用拟似然比检验来得到更精准的变点位置.在相对温和的条件下,本文证明了变点数量和位置的相合性.模拟结果和实际数据应用证明了该算法的精确性.Linear models with multiple change-points appear in a vast amount of statistical and econometric applications.In this article,the change-point detection problem is transformed into a variable selection problem by segmenting the data series and establishing a high-dimensional linear regression model with dependent observations.We apply a group orthogonal greedy algorithm(GOGA)in variable selection to adapt to the situation that the number of change-points increases with the number of observations,adding high-dimensional information criteria(HDIC)to prevent overfitting.In the first step,GOGA+HDIC+Trim is applied to the segmented data for variable selection,significantly reducing the calculation cost.The quasi-likelihood ratio test in the second step can obtain a more accurate change-point position.Under mild conditions,we prove the consistency of the number and the location of the change-points.The simulation results and the real data application also demonstrate the effectiveness of the algorithm.

关 键 词：多变点 高维回归 变量选择 组正交贪婪算法(GOGA) 高维信息准则(HDIC) 

分 类 号：O212.1[理学—概率论与数理统计]