A Local Polynomial Geographically and Temporally Weight Regression

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 three-dimensional 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