Statistical Inference Of Two Kinds Of Spatiotemporal Semi-variable Coefficient Models

With the rapid development of computer technology and the emergence of various types of data such as time series data,cross-sectional data,panel data,mixed cross-sectional data and so on,it is particularly important to study statistical methods for effectively processing large amounts of data.Spatio-temporal data with complex structure accumulated in local irregular space are widely used in many fields,such as medical disease research,temperature detection in environmental science,stock fund selection in finance and so on.Regression analysis is an important method to process data,which is divided into parametric regression and non-parametric regression.The two kinds of spatio-temporal semi-variable coefficient models studied in this paper not only have the advantages of easy interpretation of parametric regression models,but also have the flexibility and adaptability of non-parametric regression models,in addition,they also include temporal and spatial dimensions.It makes the model more adaptable to complex spatio-temporal data:Firstly,this paper introduces the linear model of spatio-temporal semi-variable coefficient part.Based on the profile least squares estimation method,the profile least squares estimation method is proposed,and the estimation expressions of variable coefficients and parameter parts are given.The asymptotic properties of the parameter parts are studied.The results of numerical simulation show that the method is effective in estimating variable coefficients and parameters in the model.Secondly,the spatio-temporal autoregressive semi-parametric model is studied,and its two-stage estimation is given based on the local polynomial method.For the multicollinearity problem caused by its temporal and spatial correlation in practice,if the least square estimation is used,there will be some bias in the estimation or lack of explanatory results.In this paper,a ridge estimation method is proposed for the multicollinearity problem of the spatio-temporal autoregressive semi-parametric model.The ridge estimation of the autoregressive variable coefficients is given,then the asymptotic normality of the ridge estimation is studied,and the bias and mean square error of the ridge estimation are obtained.The results of numerical simulation show that the multicollinearity is strong and the result of ridge estimation is better than that of two-stage estimation,while the multicollinearity is relatively weak and the two-stage estimation is better than that of ridge estimation.