具有空间相依结构的函数型数据的统计分析

现代测量技术和存储设备发展使得实时数据的收集和存储成为可能，因而在流行病监测、地理统计、空气质量监控等应用领域涌现出大量具有空间相依特征的函数型数据。该特征使得在独立结构下建立起来的许多函数型数据分析方法（如回归建模、变量选择等）受到了挑战，亟需发展新的模型和统计推断方法。鉴于此，本项目拟针对函数型数据的空间相依特征，建立空间相依函数型线性回归模型和半参数回归模型，进而研究模型的变量选择及在缺失数据下模型估计问题。基于以上研究成果分析区域性大气污染数据分析，以寻找影响区域性空气质量的主要因素。

With the development of modern measurement technologies and storage devices, it has become possible to collect and store real-time data. As a result, a large number of functional data with spatially dependent feature have emerged in many applied fields, such as epidemiological surveillance, geographical statistics, and air quality monitoring. This feature makes many functional data analysis methods (such as regression modeling, variable selection, etc.) established under the independent structure challenged, and it is urgent to develop new models and statistical inference methods. In view of this, this project aims to establish spatially dependent function linear regression models and semi-parametric regression models based on the spatially dependent features of functional data, and then study the variable selection of the model and model estimation problems when some data is missing. Based on the above research results, regional air pollution data analysis was performed to find out the main factors affecting regional air quality.