Estimation And Application Of SVMRSAR Model

It is well known that statistical inference of regression model is an important part of mathematical statistics.In recent years,the spatial data is widespread in Finance,Geology,Environment,Science and other fields,the data collected by many scholars usually has geographic characteristics,the traditional parametric regression model and non-parametric regression model can no longer analyze data with spatial characteristics efficiently.In order to solve this problem,the spatial auto-regressive model arises at the historic moment With the rapid development of research methods,this model has been studied by many scholars,in order to increase the practicability of model,some scholars put forward to add parameters of the component into spatial auto-regressive model,which improves the application range of the model,but the fixed form of parameters often lost data's flexibility,in order to increase the flexibility of the model,some experts add the variable coefficient part in the model,the variable coefficient spatial auto-regressive model is constructed.but it makes a lot of data face the "Curse of dimensionality" in the practical application.Therefore,this paper choose to neutralize the advantages of the two models,and constructed a semi-parameter spatial variable coefficient autoregressive model(SVMRSAR model).The proposed model not only meets the requirements of flexibility of the model,but also overcomes the calculation difficulties caused by high-dimensional data.In this framework,the data with spatial non-stationary characteristics can be analyzed.Therefore,the model has become a hot topic in recent years and has been applied in many fields.In this paper,the theoretical background of the semi-parameter spatial variable coefficient auto-regressive model(SVMRSAR model)is studied firstly.Secondly,the estimation methods of constant coefficient parameters and non-parameter parameters in the model are presented.Based on the B-spline function estimation method,the two-stage least square method and cross-section likelihood estimation are used to estimate the constant coefficient respectively.Then the introduction of variable selection is given,conduct hypothesis testing on obtained estimated value.The results show that the model fits well.Finally,based on the housing price data collected in December 2020,the SVMRSAR model is constructed to analyze the housing price in Yangzhou urban area,discusses the spatial influence factors of Yangzhou housing price.The study shows that the influence parameters such as greening rate,floor area rate and school distance fluctuate greatly,and the influence magnitude is higher.By comparision,hospital distance,park distance,commercial center,the number of bus stops have a small impact.It is not the primary consideration for people to buy a house,nor is it the main reason for the spatial difference of house prices.In addition,the age of a house has a significant effect on the house prices in a residential area,and it has spatial non-stationarity,as shown on the map,houses close to schools and businesses have a big revaluation space.