稳健度量选权迭代的地理加权回归研究  

Research on geographically weighted regression based on robust measurement and iterative weight

作　　者：于志英 赵阳阳[1] 张福浩[1] YU Zhiying;ZHAO Yangyang;ZHANG Fuhao(Chinese Academy of Surveying and Mapping,Beijing 100036,China)

机构地区：[1]中国测绘科学研究院

出　　处：《测绘科学》2019年第11期28-34,共7页Science of Surveying and Mapping

基　　金：国家重点研发计划课题(2016YFC0803108);国家基础测绘科技项目(2018KJ0104)

摘　　要：针对地理加权回归参数估计采用最小二乘方法,最小二乘估计易受离群值影响,导致地理加权回归模型并不稳健的问题,该文提出基于稳健度量选权迭代的地理加权回归分析方法,核心思想是通过标准化残差构造权重函数,通过迭代加权降低离群值对回归模型参数估计的影响。利用模拟数据与真实数据进行试验,分别与GWR、RGWR进行对比分析,以MSE、MAE为指标进行性能评价。模拟数据试验中,RMIWGWR模型比RGWR模型的MSE、MAE指标分别提升9.29%和8.34%;真实数据试验中,RMIWGWR模型比RGWR模型的MSE、MAE指标分别提升63.88%和38.45%。试验表明:该方法可改善粗差存在环境下地理加权回归模型参数估计精度,提升模型拟合效果。The least square method is used to estimate the parameters of geographically weighted regression(GWR).It is sensitive to outliers,resulting in the GWR that is not robust.In this paper,geographically weighted regression based on robust measurement and iterative weight(RMIWGWR)is proposed.The core idea is to construct the weight function by standard residuals and reduce the influence of outliers on the parameter estimation by iterative weighting.In the simulation data test,the MSE and MAE indicators of the RMIWGWR model were 9.29% and 8.34% higher than those of the RGWR model.In the real data test,the RMIWGWR model increased by 63.88% and 38.45%,respectively,compared with the MSE and MAE indicators of the RGWR model.The results demonstrate that RMIWGWR can improve the parameter estimation accuracy of GWR in the rough environment and improve the model fitting effect.

关 键 词：地理加权回归 选权迭代 粗差剔除 参数估计 

分 类 号：P208[天文地球—地图制图学与地理信息工程]