带有自相关结构误差的多元函数型回归模型的变量选择  

Variable Selection in Multiple Functional Regression Model with Autoregressive Errors

作　　者：李倩 谭祥勇 王黎明[3] LI Qian;TAN Xiangyong;WANG Liming(School of Economics,Nanjing University of Posts and Telecommunications,Nanjing,210003,China;School of Statistics and Data Science,Jiangxi University of Finance and Economics,Nanchang,330013,China;School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai,200433,China)

机构地区：[1]南京邮电大学经济学院,南京210003 [2]江西财经大学统计与数据科学学院,南昌330013 [3]上海财经大学统计与管理学院,上海200433

出　　处：《应用概率统计》2024年第4期588-607,共20页Chinese Journal of Applied Probability and Statistics

基　　金：江苏省高校自然科学基金项目(批准号:21KJD110004);江苏省高校哲学社会科学项目(批准号:2021SJA0099);南京邮电大学科研启动基金项目(批准号:NYY220017);国家自然科学基金项目(批准号:12201260,12201413);江西省自然科学基金重点项目(批准号:20212ACB201006);江西省自然科学基金资助项目(批准号:20212BAB211010);中国博士后科学基金资助项目(批准号:2022M711425)资助.

摘　　要：多元函数型回归模型是经典多元线性模型的有益扩展.本文研究带有自相关结构误差的多元函数型回归模型的变量选择.我们基于Group SCAD(smoothly clipped absolute deviation)惩罚研究了模型中函数型协变量的变量选择和误差项的自相关阶数的确定问题.此外,我们在一定的正则性条件下证明了估计量的选择相合性和渐近正态性,并通过数值模拟说明提出方法在有限样本下具有良好性质.Multiple functional regression models are a useful extension of classical multiple linear model.This paper focuses on the variable selection of multiple functional regression models with autoregressive errors.Based on Group SCAD(Smoothly Clipped Absolute Deviation)penalty,we study the variable selection of functional covariates and the order of the autoregressive error term simultaneously.In addition,we provide the selection consistency and asymptotic normality under mild conditions,and demonstrate its performance through simulation studies.

关 键 词：多元函数型回归模型 自回归误差 Group SCAD 选择相合性 

分 类 号：O213.9[理学—概率论与数理统计]