基于copula函数的纵向数据复合分位数回归及变量选择  

Copula based composite quantile regression for longitudinal data and variable selection

作　　者：王康宁 李劭珉 林路 Kangning Wang;Shaomin Li;Lu Lin

机构地区：[1]山东工商学院统计学院,烟台264005 [2]北京大学光华管理学院,北京100871 [3]山东大学金融研究院,济南250100

出　　处：《中国科学：数学》2020年第8期1097-1116,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11901356和11231005);山东省自然科学基金(批准号:ZR2017BA002)资助项目。

摘　　要：复合分位数回归(composite quantile regression)具有稳健性好和估计效率高的优势,所以其经常被用来替代均值回归.众所周知,纵向数据具有组内相关的特点,如果估计过程中能正确地利用组内相关性,则可以显著地提高估计效率.因此,探讨纵向数据复合分位数回归中如何使用相关性是一个有意义的问题.本文首先利用copula函数方法构建纵向数据复合分位数回归的组内协方差矩阵,进而基于构建的协方差矩阵,提出一个无偏且有效的基于copula函数的复合分位数回归估计方程;进一步,为了进行变量选择,利用基于copula函数的估计方程,提出一个光滑门限(smooth-threshold)的复合分位数回归估计方程方法.本文提出的方法具有很高的灵活性,而且提高了估计的效率.理论结果以及数值模拟和实际数据分析都验证了本文的方法.Composite quantile regression(CQR)is a good alternative of the mean regression,because of its robustness and efficiency.As is well known,longitudinal data is characterized by within-subject correlation,and if the correlation can be correctly incorporated in the estimation procedure,the efficiency will be improved.Hence,how to specify the correlation structure in CQR with longitudinal data is an interesting issue.We propose a new approach that uses copula to account for intra-subject dependence,and by using the copula based covariance matrix,efficient and unbiased CQR estimating equations are constructed.As a specific application,a smooththreshold CQR estimation equation is proposed for variable selection.Our proposed new methods are flexible,and can provide efficient estimation.The properties of the proposed methods are established theoretically,and assessed numerically through simulation studies and real data analysis.

关 键 词：复合分位数回归 纵向数据 COPULA函数 有效性 变量选择 

分 类 号：O212.1[理学—概率论与数理统计]