Collaborative Research: Non-Parametric Inference of Temporal Data

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.