异方差混合地理加权回归模型的正交投影估计  

Orthogonality Projection-based Estimation for Mixed Geographically Weighted Regression Models With Heteroscedasticity

作　　者：古丽斯坦·库尔班尼牙孜 孟丽君 田茂再[1,2,3] Gulistan Kurbanyaz;Meng Lijun;Tian Maozai(School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012,China;Center for Applied Statistics,Renmin University of China,Beijing 100872,China;School of Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]新疆财经大学统计与数据科学学院,乌鲁木齐830012 [2]中国人民大学应用统计科学研究中心,北京100872 [3]中国人民大学统计学院,北京100872

出　　处：《统计与决策》2024年第15期52-58,共7页Statistics & Decision

基　　金：新疆维吾尔自治区社会科学基金项目(22VZX021);新疆财经大学高层次人才专项项目(2023XGC006);新疆维吾尔自治区普通高校人文社会科学重点研究基地基金项目(XJEDU2023P011)。

摘　　要：文章针对误差项存在空间异方差的混合地理加权回归模型,提出了一种新的估计方法。该方法将正交投影、局部线性估计和广义最小二乘估计的思想相结合,能够单独对模型中的常数系数、系数函数和方差函数进行估计。通过数值模拟对所提方法的性能进行验证。模拟结果表明,所提方法比现有的再加权估计方法更具优势。最后,基于城镇居民文化消费水平及其影响因素的实证分析验证了所提方法的实用性。This paper proposes a new estimation method for the mixed geographically weighted regression models with spatial heteroscedasticity of error terms.This method combines the idea of orthogonal projection,local linear estimation,and generalized least squares estimation to separately estimate the constant coefficients,coefficient functions and variance functions in the model.The performance of the proposed method is verified through numerical simulation.The simulation results show that the proposed method performs better than existing reweighted estimation methods.Finally,the practicality of the proposed method is verified through empirical research based on the cultural consumption and influencing factors of urban residents.

关 键 词：混合地理加权回归模型 正交投影估计 空间异方差性 局部线性估计 

分 类 号：O212[理学—概率论与数理统计]