高维空间相依数据的Expectile回归分析  

Expectile regression analysis of high-dimensional spatially dependent data

作　　者：刘宣 马海强 盛志雁 罗良清[2] Xuan Liu;Haiqiang Ma;Zhiyan Sheng;Liangqing Luo

机构地区：[1]南昌师范学院数学与信息科学学院,南昌330032 [2]江西财经大学统计与数据科学学院,南昌330013

出　　处：《中国科学：数学》2024年第4期617-646,共30页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12161042);中国博士后面上项目(批准号:2019M662262);国家社科基金重大项目(批准号:21&ZD150);江西省博士后特别资助项目(批准号:2021KY18);江西省教育厅科技项目(批准号:GJJ200522和GJJ202603)资助项目。

摘　　要：空间数据的异质性、空间权重的内生性和解释变量的高维特征会给空间相依数据分析带来重大挑战.本文基于Expectile回归的稳健估计优势和惩罚压缩的有效降维能力,分别在外生空间和内生空间权重矩阵条件下,给出高维空间滞后模型未知参数的两步与三步惩罚Expectile估计,并在常规正则条件下证明所提出估计的相合性和变量选择的Oracle性质.数值模拟显示,两步估计法能有效处理外生空间权重矩阵条件下的稳健统计问题,同时三步估计法在外生空间和内生空间权重条件下均有优良表现.最后,通过分析我国市域空气质量与经济发展的关系,进一步验证所提出方法的有效性.There are great challenges to the analysis of spatially dependent data with the heterogeneity,the endogeneity of spatial weights,and the high-dimensional characteristics of explanatory variables.Based on the robust estimation advantage of Expectile regression and the effective dimensionality reduction ability of penalty compression,we give the two-step and three-step penalty Expectile estimation of unknown parameters of high-dimensional spatial lag models under the exogenous and endogenous spatial weight matrices respectively,and prove the consistency of the proposed estimation and the Oracle property of variable selection under conventional regularization conditions.The numerical simulation demonstrates that the two-step estimation method can work well with the robust statistical problem under the exogenous spatial weight matrix,and the three-step estimation method has excellent performance under the exogenous and endogenous spatial weights.Finally,the effectiveness of the proposed method is further verified by analyzing the relationship between the urban air quality and the economic development in China.

关 键 词：空间滞后模型 Expectile回归 变量选择 内生性 高维数据 

分 类 号：O212.1[理学—概率论与数理统计]