Collaborative Research: Non-Parametric Inference of Temporal Data

该项目是由需要解决在不同领域的调查，包括环境科学，流行病学和经济学等驱动。对极端天气事件（如热带风暴）的研究要求气象学家确定随着时间的推移，更强的热带风暴是否比中等或低级别的热带风暴发生得更频繁。研究COVID-19传播性和严重程度的流行病学家利用临床实验室数据来评估趋势模式。在调查海洋污染水平时，地球科学家收集动物体内汞浓度的数据，以确定多年来汞浓度是否有上升趋势。该研究项目的主要目标是改进解决这些问题的方法，并有效地向科学界和公众传播研究结果。可以根据调查结果做出更明智的决定。该项目还包括通过研究生积极参与研究来培训和指导他们。该研究团队旨在开发创新的统计方法来研究时间观察或时间索引的多样本数据，这些数据包括在不同时间点对不同受试者进行的测量。这样的数据不属于传统的单变量或高维时间序列，因为在不同时间点的测量可能没有固有的联系。研究人员和合作者将开发一个系统的渐近理论来解决这一挑战，以估计和推断时间上观察到的多样本数据。他们将建立一致性，渐近正态性，并为各种相关的统计和研究同时置信带和变点分析极值分布理论。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

This project is driven by the need to address inquiries in diverse fields, including environmental sciences, epidemiology, and economics among others. The study of extreme weather events, such as tropical storms, requires meteorologists to determine whether more potent tropical storms occur more frequently than mid or low-level tropical storms over time. Epidemiologists studying the transmissibility and severity of COVID-19 utilize clinical laboratory data to evaluate the pattern of the trends. In investigating sea pollution levels, earth scientists gather data on mercury concentration in animals to determine whether there has been a rising trend in mercury concentration over the years. The primary objective of this research project is to enhance the methods used to tackle these questions and effectively communicate findings to the scientific community and the public. More informed decisions can be made based on the findings. This project also involves training and mentoring graduate students through their active involvement in the research. The research team aims to develop innovative statistical methods to study temporally observed or time-indexed multi-sample data, which consist of measurements of different subjects made at different time points. Such data do not fall within the conventional univariate or high-dimensional time series since measurements at different time points may not have an inherent connection. The investigators and collaborators will develop a systematic asymptotic theory to address this challenge to estimate and infer temporally observed multi-sample data. They will establish consistency, asymptotic normality, and an extremal distribution theory for various associated statistics and study simultaneous confidence bands and change points analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.