Selection And Application Of Adaptive Bandwidth Matrices Of Spatially Varying Coefficient Model

In many disciplines in life,the data collected always contains specific spatial location information,this type of data with spatial location attributes is called spatial data.Spatial data is a powerful tool to reveal spatial effects.Two important sources of spatial effects include spatial dependence(spatial correlation)and spatial heterogeneity(spatial non-stationarity).The existing spatially varying coefficient model for solving spatial data problems starts with the isotropy of spatial data,and selects a bandwidth h for spatial coordinates,giving the same weight to two dimensions of data.And spatial data usually presents anisotropy in geographic location,with different distribution directions and uneven distribution.Based on this consideration,this paper introduces bandwidth matrices into the weight matrix of the spatially varying coefficient model.The bandwidth matrices are not only from the geographic location two dimensions of(u,v)considered,and the kernel smooth direction is introduced,which can better reflect the spatial heterogeneity.First of all,this paper introduces the local linear GWR(Geographically weighted regression)method of the spatially varying coefficient model.The two-dimensional unconstrained bandwidth matrices are introduced into the weight matrix of the spatially varying coefficient model,and the two-dimensional Gauss kernel function is used to derive the weight matrix under the two-dimensional kernel function to get the parameter estimation.Through simulation experiments,the parameter estimation value obtained under this method is compared with the parameter estimation value obtained under the ordinary one-dimensional bandwidth.The coefficient function surfaces obtained by the two situations are very close to the real surface.The residual comparison chart shows that the residuals of the estimated value obtained under the one-dimensional bandwidth are relatively concentrated,while the residuals of the estimated value obtained under the bandwidth matrices will have outliers.The table data shows that selecting two-dimensional bandwidth matrices for(u,v)is more accurate than the estimated value obtained by selecting a bandwidth,that is,it is necessary to consider the anisotropy of the data in the spatial position;at the same time,using the Plug-in(Plug-in)method to select the bandwidth matrices instead of the GCV(Generalized Cross-Validation)method to select a single bandwidth can reduce the number of data traversals and improve the computational efficiency to a certain extent;Then,using relevant data such as the single-period vegetation cover index in the Yili area in 2011,the relationship between the vegetation cover index and climate factors such as temperature and precipitation was studied,and the spatial impact of temperature and precipitation on the vegetation cover index was revealed.Finally,considering that the adaptive bandwidth matrices are more flexible than the global bandwidth matrices,the adaptive bandwidth matrices are introduced into the weight of the spatially varying coefficient model to solve the problem of large residual errors in the parameter estimates obtained from the global bandwidth matrices,combining with two-dimensional Gauss kernel function.The weight matrix under the adaptive bandwidth matrices is derived for parameter estimation.Simulation experiments show that the introduction of the adaptive bandwidth matrices improve the situation of outliers in the parameter estimation obtained from the global bandwidth matrices,and uses the 2011 Yili area vegetation cover index data to analyze again.