Statistical Inference for Functional Data in Time Series and Survey Sampling: Theory and Methods

复杂的数据收集设施通常产生以曲线、图像或形状的形式表示的一组函数的数据。函数数据分析在理论和方法上的发展为我们提供了重要的分析工具，以解决在许多重要领域遇到的挑战性问题。在拟议的研究中，研究者继续构建和丰富功能数据的理论和方法。这项提议的目标是开发强大的统计工具，用于分析时间序列和调查抽样框架中的功能数据。提出了四个相关的研究课题以供研究。对于每个项目，将研究估计器的统计特性、由基本模型管理的统计推论以及推论的理论特性。所提出的方法可用于估计相依函数数据的全局数量，量化和可视化估计量的可变性，并对总体数量的形状进行全局推断。随着复杂(如纵向、功能性、异构性或相关性)特征的“大数据”在许多研究领域越来越多地可供公众使用，该提案是解决分析此类数据类型的挑战的一种工具。拟议项目的成功为处理时间和空间上的大型和复杂的结构数据提供了有效和实用的工具，代表着统计分析理论和方法的进步。拟议的研究对整个社会的好处包括针对具有复杂特征的大数据的新方法和推理工具。统计学家、调查研究人员，甚至更广泛的气候学、卫生、经济学、工程学、环境研究、气象学、行为和社会科学的研究人员，都对这些主题感兴趣。

Sophisticated data collection facilities often produce data which are a set of functions, represented in the form of curves, images or shapes. The development of functional data analysis in theory and methodology has provided us important analytical tools to address challenging problems encountered in many important fields. In the proposed research, the investigator continues to build and enrich the theory and methodology of functional data. This proposal targets the development of powerful statistical tools for analyzing functional data in time series and survey sampling frameworks. Four related research topics are proposed for investigation. For each project, statistical properties of the estimators, statistical inferences governed by the underlying models, and theoretical properties of the inferences will be studied. The proposed methods can be used to estimate global quantities for dependent functional data, quantify and visualize the variability of the estimators, and make global inferences on the shape of the population quantities. With "big data" of complex (such as longitudinal, functional, heterogeneous, or correlated) features becoming increasingly available for public use in many research areas, this proposal is one vehicle to address the challenges of analyzing such types of data. The success of the proposed projects provides effective and practical tools for dealing with large and complex structural data over time and space, representing advances in the theory and methodology of statistical analysis. The benefits to society at large of the proposed research include new methodology and inference tools for big data with complex features. These topics are of interest to statisticians, survey researchers, and indeed, more broadly for researchers in climatology, health, economics, engineering, environmental studies, meteorology, behavioral and social sciences.