具有内生权重的高维空间滞后分位数模型的估计和变量选择  

Estimation and Variable Selection for Quantile Regression of High-Dimensional Spatial Dependent Data with Endogenous Spatial Weight Matrix

作　　者：马海强 盛志雁 刘宣 陈建宝 Haiqiang Ma;Zhiyan Sheng;Xuan Liu;Jianbao Chen(School of Statistics and Data Science,Jiangxi University of Finance and Economics,Nanchang 330013,P.R.China;School of Mathematics and Information Science,Nanchang Normal University,Nanchang 330032,P.R.China;School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,P.R.China)

机构地区：[1]江西财经大学统计与数据科学学院,南昌330013 [2]南昌师范学院数学与信息科学学院,南昌330032 [3]福建师范大学数学与统计学院,福州350117

出　　处：《数学学报(中文版)》2025年第2期240-267,共28页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金资助项目(12161042);国家社会科学基金项目(22BTJ024);中国博士后科学基金面上项目(2019M662262);江西省博士后特别资助项目(2021KY18);江西省自然科学基金资助项目(20242BAB26002,20242BAB25020);江西省教育厅科技项目(GJJ200522)。

摘　　要：随着大数据技术的发展,空间数据的维数越来越高,并且数据中经常存在内生性和异质性等问题,为了对高维空间相依数据进行稳健分析,本文提出了具有内生权重的高维空间滞后分位数回归模型,通过组合控制变量法和高维稳健方法给出了三步惩罚的分位数估计算法,并证明了所得估计量的相合性、渐近正态性和变量选择的Oracle性质.数值模拟和对全国284个地级市的房价数据分析验证了本文所提模型和估计方法具有稳健的优良性质.With the development of big data technology,the dimensionality of spatial data is becoming higher and higher,and the endogeneity and heterogeneity of data often exist simultaneously.In this paper,we propose a quantile regression model of high-dimensional spatial dependent data with endogenous spatial weight matrix so as to analyze high-dimensional spatial dependent data robustly.We then develop a three-step penalized quantile estimation procedure through combining the instrumental variable method,variable selection method with robust statistic method,and establish the consistency and the asymptotic normality of the corresponding estimators.In addition,the oracle theoretical properties of variable selection are derived under some mild conditions.At last,we investigate the effectiveness and robustness of the proposed model and method through simulations and an application to housing prices in 284 prefecture-level cities across the country.

关 键 词：高维空间相依数据 内生权重矩阵 异质性 分位数回归 渐近理论性质 

分 类 号：O177.2[理学—数学]