具有复杂相关结构时空模型的非参数估计与预测

Spatio-temporal data analysis is widely required in enviromenal science,earth-science, medical science, economics and many other fields. Spatio-temporal data usually involve complex correlated structures. This project will study how to propose more efficient nonparametric estimation and prediction methods for spatio-temporal models with complex correlation structures as well as the application problems. At first,this project will study statistical inference of spatio-temporal models with specific correlation structures, including proposing effective statistics and investigating their large sample properties ; Secondly, this project will study the estimation and prediction problems for spatio-temporal models with general correlation structures; Finally, the proposed approaches will be applied to practical problems. Due to the complex correlation of the spatio-temporal data and the essential difference between space and time, the research of these problems bears some hard difficulties. So far, the existing statistical methods have been applied mechanically to spatio-temporal data widely, but it lacks of the methods that are suitable for spatio-temporal data and lacks of theoretical supports of related statistical inference. In view of the complex spatio-temporal correlation and the essential difference between space and time, this project will use the theory of function approximation, mathematical programming and the iterative approach. It is expected that we can solve some important issues in spatio-temporal data statistics, and thus promote more satisfactory solutions of corresponding practical problems, and worked out a new way to research these kind complex issues through this study.

时空数据统计分析在环境科学、地球科学、医药领域、经济科学等许多领域中有重要应用。时空数据大都具有复杂的相关结构。本项目研究具有复杂相关结构的时空模型的有效非参数估计、预测以及应用问题。首先研究有具体相关结构的时空模型的统计推断，包括提出有效的统计量及其大样本性质；其次研究具有一般相关性结构的时空数据的估计与预测问题；最后将我们的方法应用到实际问题中。由于时空数据的复杂相关性和时间与空间的本质区别，使这些问题的研究产生很大的困难。目前现有统计方法在时空数据中的套用已广泛展开，尚缺乏适合于时空数据特点的方法和作为统计推断的理论支持的统计量性质的成果。本项目将利用函数逼近和数学规划的理论以及迭代的方法来进行研究。期望通过这一研究，解决时空数据统计中一些重要问题，使相应实际问题得到更完满的解决，并摸索出一条研究这类复杂问题的新路子。

时空数据统计分析在环境科学、地球科学、医药领域、经济科学等许多领域中有重要应用。时空数据大都具有复杂的相关结构。本项目研究具有复杂相关结构的时空模型的有效非参数估计、预测以及应用问题。首先研究有具体相关结构的时空模型的统计推断，包括提出有效的统计量及其大样本性质；其次研究具有一般相关性结构的时空数据的估计与预测问题；最后将我们的方法应用到实际问题中。由于时空数据的复杂相关性和时间与空间的本质区别，使这些问题的研究产生很大的困难。目前现有统计方法在时空数据中的套用已广泛展开，尚缺乏适合于时空数据特点的方法和作为统计推断的理论支持的统计量性质的成果。本项目将利用函数逼近和数学规划的理论以及迭代的方法来进行研究。考虑相关性以提高估计的精度是一个研究内容丰富、很有挑战性的课题，它不但具有理论上的研究价值，也具有更直观的实际意义。