广义函数型部分空间变系数模型估计与应用

Estimation of Generalized Functional Partial Spatial Varying Coefficient Models and Its Application

针对函数型数据与空间数据嵌套融合的统计建模问题,提出了广义函数型部分空间变系数模型(GFPSVCMs),利用函数型主成分基函数和基于三角剖分的二元惩罚样条逼近该模型中的斜率函数和二元系数函数,采用最大化惩罚拟似然的方法实现模型参数估计,并给出了一种带惩罚的迭代重加权最小二乘迭代算法(GFPSVCMs-PIRLS)进行参数求解.数值模拟表明所提出的模型在不同设定下的表现出了良好的性能.实证分析部分,利用我国13个省份包含151个地市州的空气质量和日均气温数据分析了空气质量的影响因素,评估了所提出模型在空气质量研究领域中的应用价值和预测性能.

Aiming at the statistical modeling problem of nested fusion of functional data and spatial data,we proposed a generalized functional partial spatial variables model(GFPSVCMs),and the slope function and bivarite coefficient function in the models are approximated by using the functional principal component basis function and the bivarite penalty spline based on triangulation,and the parameter estimation is realized by maximizing the penalty quasi-likelihood,and a Penalty Iterative Re-weighted Least Squares iterative algorithm(GFPSVCMs-PIRLS)is given for parameter solving.Numerical simulations show that the proposed model exhibits good perfor-mance at different settings.In the empirical analysis section,we analyzed the influenc-ing factors of air quality by using the air quality data and average daily temperature data of 13 provinces in China,including 151 prefectures,cities,and states,and eval-uated the application value and prediction performance of the proposed model in the field of air quality research.