The Estimation Of Semi-parametric Geographically And Temporally Weighted Regression Model And Its Statistical Inference

With the expansion of the scop of statistical research and application,the data witch have space position information and time attributes caused the researchers attention.in spatio-temporal data analysis the main research is regression relevance and regression nonstationary.so spatially and temporally weighted regression model plays an important role in spatio-temporal data analysis.spatially and temporally weighted regression model is the direct expansion of geographically weighted regression model.in the varying coe?cient regression model by means of suppose regression coe?cient is the function of geographic position and observation time,the data coordinates of space and time embedded in the regression model,provide the e?ective analysing way to analysis the nonstationary of regression relationship.in this paper bu means of local linear regression techniques,analyzed the spatially and temporally weighted regression model,semi parametric spatially and temporally weighted regression model and its statistical inferences.the main innovation points is below:(1)the varying coe?cient regression model,geographically weighted regression model are introduced and the local linear estimation method of geographically weighted regression model is given.the recent research situation of geographically and temporally weighed regression model and its GTWR method.local linear estimation method of geographically and temporally weighed regression model based on local linear technique is narrated.(2)a new type of semi-parametric geographically and temporally weighed regression model regression model is proposed for describing more extensive that can describe broader type of regression spatial and temporal structures of the coe?cient functions.Two-step estimation procedure for this model is suggested based on the local linear fitting technique and the estimation of both the parametric and the nonparametric coe?cient functions are obtained.(3)Based on local linear fitting technique, hypothesis test method on geographically and temporally weighed regression model and semi-parametric geographically and temporally weighed regression model are given.based on the so-called generalized likelihood ratio statistics are proposed respectively for testing the hypothesis that all the coe?cients are linear function of spatial and temporal coordinates and the hypothesis that some of the coe?cients are linear combinations of some known functions of spatial and temporal coordinates.