Parameter Estimation Of Generalized Spatio-temporal Autoregressive Model With Variable Coefficients And Its Application

With the advent of big data's era,the amount of data has increased greatly,and they are often classified and saved in order to make it easier to manage and use them.If divided by time or space,the collected data can be divided into spatial data and temporal data,collectively called spatio-temporal data.Through the research and analysis of the spatio-temporal data,we can better measure the influence degree of different spatio-temporal positions on a fixed point.In recent years,the non-parametric model method is becoming more and more perfect,and the variable coefficient model has attracted more and more scholars' attention.In order to solve the spatio-temporal data problem,the spatio-temporal variable coefficient regression model was bred.However,this spatio-temporal model is mostly used to solve continuous spatio-temporal data problems,but few researches on discrete spatio-temporal data problems.In this paper,a new spatio-temporal variable coefficient model for spatio-temporal discrete data is proposed and applied to the study of spatio-temporal AIDS data.Firstly,the parameters of the generalized spatio-temporal variable coefficient regression model are solved by the local linear GWR estimation and iterative weighted least squares estimation,and the simulated surface of coefficient function is obtained from the simulation experiment.It is found that the generalized spatio-temporal variable coefficient regression model is more suitable for the spatio-temporal discrete data than the generalized spatial variable coefficient regression model.Then,the parameters of the generalized spatio-temporal autoregressive model are solved by using GWR estimation,Newton-Raphson iteration and Fisher scaling method,and the simulation surface of coefficient function is also obtained by simulation experiment.The comparison shows that under the same parameter estimation method,the generalized spatio-temporal variable system is obtained.In this paper,using the generalized spatio-temporal variable coefficient regression model analysis of China's 31 provinces,municipalities and autonomous regions in 2011-2016 years the incidence of AIDS changes of time and space,and discuss the impact of the four macro factors to the incidence of HIV/AIDS and temporal variation characteristics.At the same time,the time-and-space change of AIDS in10 mainland countries in the southern part of Africa in the year 2011-2016 is analyzed by using the generalized time-space variable coefficient self-regression model,as well as the spatial and temporal change characteristics of the effect of per capita GDP and population density on the incidence of AIDS.Research found that: 1)there were obvious changing trends and spatio-temporal aggregation in the areas with high incidence of AIDS,2)different macro-factors had different intensity of influence on the incidence of AIDS in different regions at different times;3)the spatio-temporal distribution of AIDS incidence is closely related to the change of macro-factors.