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的数据是一组函数，以曲线、图像或形状的形式表示。功能数据分析在理论和方法上的发展为我们解决许多重要领域中遇到的挑战性问题提供了重要的分析工具。在拟进行的研究中，研究者将继续构建和丰富功能数据的理论和方法。本建议的目标是开发强大的统计工具来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。对于每个项目，将研究估算器的统计特性、由基础模型支配的统计推断以及推断的理论特性。所提出的方法可用于估计依赖函数数据的全局量，量化和可视化估计量的变异性，并对种群数量的形状进行全局推断。随着复杂的“大数据”（如纵向的、功能的、异构的或相关的）特征在许多研究领域越来越多地为公众使用，本提案是解决分析这类数据的挑战的一种工具。拟议项目的成功为处理随时间和空间变化的庞大而复杂的结构数据提供了有效和实用的工具，代表了统计分析理论和方法的进步。所提出的研究对整个社会的好处包括具有复杂特征的大数据的新方法和推理工具。这些主题是统计学家、调查研究人员感兴趣的，实际上，更广泛地说，是气候学、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感兴趣的。

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.