A Study On Local Polynomial GWR Model And Its Application

Geographically weighted regression(GWR)is a spatial regression analysis method that can effectively detect the spatial non-stationarity.Its parameters are usually estimated by weighted least squares.However,estimated results obtained by weighted least squares have obvious boundary effect,and the achieved accuracy is low for coefficients estimation with different smoothness.Moreover,in real data,the gross error of the observations can seriously interfere with the accuracy of the weighted least squares estimation,resulting in poor robustness of GWR models.But the local polynomial estimation can automatically correct boundary effect,and polynomial functions of different orders can be used to approximate coefficients of different smoothness.This paper focuses on the local polynomial GWR model,its modeling process and improved methods of parameters estimation.The effectiveness of the model can be validated based on simulation experiments and real data.The main study of this paper includes:(1)The local polynomial GWR model is introduced and analyzed.We introduce firstly the modeling process of GWR models.Based on a Taylor expansion formula,the local linear GWR model is extended to the second-order and third-order local polynomial GWR models.Through simulation experiment,it is validated that local polynomial GWR model can solve the boundary effect and improve the accuracy of parameters estimation.Finally,the effectiveness of the local polynomial GWR model is validated based on the real price data of residential commercial housing.(2)We study the two-step estimation of the local polynomial GWR model.Based on local polynomial GWR model,we use polynomial functions of different orders to approximate the coefficient function of different smoothness,and give a two-step estimation method to estimate corresponding parameters.Simulation experiments show that the two-step estimation can improve the accuracy of parameters estimation.Finally,the effectiveness of improved model can be validated based on the real data of PM2.5 concentration.(3)Our research is the robust iteratively reweighted estimation of the local polynomial GWR model.Our approach combines with the robust iteratively reweighted estimation method,and use the reliability-weighted function to gradually reduce the impact of the gross error and improve the robustness of the model.It is validated from a simulation experiment that the robust iteratively reweighted estimation of local polynomial GWR model has better accuracy of parameters estimation.Finally,its effectiveness is validated by the real data of population distribution.