【摘要】 基于加权最小二乘估计的时空地理加权回归方法,在随机项方差相同且最小的假设条件下估计回归参数和拟合值,由于没有考虑时空分析中异方差影响而导致估计结果存在一定偏差。局部多项式估计是一种消除异方差影响的非参数估计方法。本文在局部多项式估计原理基础上,提出了局部多项式时空地理加权回归方法。它是采用三元一阶泰勒级数展开式重构时空回归系数和自变量矩阵,进而建立满足高斯-马尔可夫独立同分布假定要求的新模型,利用新模型回归系数估计值、拟合值以及新模型与原模型的关系,可得到原模型回归系数估计值和拟合值。本文采用模拟数据和真实数据进行试验,以GTWR与局部线性地理加权回归作为对比方法,从方法适用性、整体估计效果、回归系数估计偏差和拟合优度、整体估计偏差等方面分析了LPGTWR方法性能,有效证明了LPGTWR方法能消除异方差影响提升估计精度。更多还原

【Abstract】 Geographically and temporally weight regression(GTWR)estimates regression coefficients and fitted value by weighted least squares(WLS),which under the assumption of the same minimum random variance.As without considering the spatio-temporal heteroscedasticity,it may reduce the accuracy of estimation.Local polynomial estimation is a nonparametric estimation method to eliminate heteroscedasticity in statistics.On the basis of the local polynomial estimation,the local polynomial geographically and weight regression temporally(LPGTWR)approach is proposed in this paper.It reconstructs the spatio-temporal coefficients using threedimensional Taylor Series in order to satisfy the Gauss-Markov assumption of independent identical distribution.Then estimate the regression coefficients and fitting value using weighted least squares.The experiments use both simulated data and real data to compare LPGTWR,GTWR and local linear-fitting-based geographically weight regression(LGWR).Experiments using simulated data showed that LPGTWR can significantly improve the accuracy of estimation not only in goodness-of-fit of the fitted value,but also in reducing bias of the coefficient estimation and the estimation.It is useful by adopting LPGTWR to eliminate heteroscedasticity effect and improve estimation accuracy.更多还原