MSE values of the four functional spatial models.

The Fenwei Plain is listed as one of the most serious air pollution regions in China, along with Beijing-Tianjin-Hebei and Yangtze River Delta regions. This paper proposed a functional data analysis method to study the environmental pollution problem in the Fenwei Plain of China. Functional spatial autoregressive combined (FSAC) model with spatial autocorrelation of both the response variable and error term is developed. The model takes the SO2 concentration of Fenwei Plain as the dependent variable and the dew point temperature as the independent variable and realizes the maximum likelihood estimation using functional principal component analysis to obtain the asymptotic properties of parameter estimation and the confidence interval of the slope function. According to the findings of the empirical analysis of the Fenwei Plain, the SO2 concentration has significant seasonal characteristics and has decreased year over year for three years in a row. Winter is the season with the highest concentration on the Fenwei Plain, followed by spring and autumn, while summer is the season with the lowest concentration. Winter also has a high spatial autocorrelation. The FSAC model is more effective at fitting the concentration and dew point temperature of the Fenwei Plain in China because its mean square error (MSE) is significantly lower than that of the other models. As a result, this paper can more thoroughly study the pollution problem on the Fenwei Plain and offer guidance for prevention and control.汾渭平原与京津冀、长江三角洲地区一同被列为中国大气污染最为严重的区域之一。本研究提出一种函数数据分析方法，用于探究中国汾渭平原的环境污染问题。构建了同时考虑响应变量与误差项空间自相关性的函数空间自回归组合（FSAC）模型。该模型以汾渭平原的二氧化硫（SO₂）浓度作为因变量，露点温度作为自变量，通过函数主成分分析实现极大似然估计，以此得到参数估计的渐近性质与斜率函数的置信区间。基于汾渭平原的实证分析结果显示，该区域二氧化硫浓度具备显著季节特征，且已连续三年逐年下降。冬季为汾渭平原浓度最高的季节，其后依次为春季与秋季，夏季浓度最低；同时冬季的空间自相关性较强。相较于其他模型，本研究的FSAC模型均方误差（MSE）显著更低，因此能够更精准地拟合中国汾渭平原的二氧化硫浓度与露点温度数据。本研究可更深入地剖析汾渭平原的环境污染问题，并为污染防控工作提供决策指引。