Spatial Self-regression Model With Multiple Function Arguments And Its Application In Ozone Pollution Monitoring

At the beginning of a new journey of building socialism with Chinese characteristics,a large number of massive data of various types were collected and stored,and the types in the real problem were many more complex,and one of the data presented a functional curve form,called functional data.The classic pattern of functional data processing is the functional linear regression model.In general,the use of functional linear regression models is mainly based on sample-independent assumptions,but due to the large number of geographical proximity or trade exchanges between countries or regions in some surveys of spatial economic and social development,air quality monitoring,etc.In order to make better use of these adjacent related statistics for classification,this paper mainly uses autoregressive methods to place adjacent explanatory variables as independent variables in the model.On this basis,the application of spatial autoregression model with multiple functional independent variables and traditional regression model with multiple functional independent variables in the monitoring of ozone pollution in the main urban area of Chongqing is studied.First,consider the preprocessing of functional data.For function class data,its function expressions are derived from observations of discrete values recorded.Therefore,before analyzing the functional data information,the original discrete data information collected should first be smoothed out,that is,the raw The discrete data of the transformation is a smooth function.In view of this,this article focuses on the analysis of Fourier basis functions and B-spline basis functions,and examines the characteristics of scatter plots through the analysis of the resulting discrete data,as well as the scatter plots depicting the data Then choose the appropriate basis function: Fourier is best suited for the periodic function,and the B-spline basis function is the opposite.In this paper,the application of ozone pollution monitoring in the main urban area of Chongqing,after the analysis of the temporal and spatial distribution characteristics of ozone values,it can be found that there is a great periodicity between ozone values,so the Fourier basis function is used in this article to smooth the raw data.Then,the model is built,parameter estimation and its simulation study is carried out.In this paper,first of all,a spatial autoregression model with multiple functional independent variables and a traditional regression model with multiple functional independent variables are established based on the spatial functional linear regression model,and the scalar explanatory variables are also added to the model;secondly,the parameters and slope functions of the model are estimated by the functional principal component analysis method and the maximum likelihood estimation method.Then,using the software to set different parameters and multiple functional and scalar independent variables,the constructed spatial model was simulated;the results showed that due to the increase in the spatial autoregression coefficients The model constructed in this paper fits more efficiently.Finally,an empirical analysis is conducted.First,the spatial and temporal effects are carried out on the monitoring data of ozone pollution in the main urban area of Chongqing The analysis showed that ozone pollution had strong seasonal variation and significant spatial autocorrelation,and then,using the monitoring data,the spatial autoregressive model with multiple functional independent variables and the traditional functional regression model were compared,and the results showed that the error of considering spatial effects was smaller than not considering spatial effects.The effect is better.