The National Science Foundation (NSF) awarded a $155,372 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program to the University of Illinois. The grant, titled "COLLABORATIVE RESEARCH: STATISTICAL INFERENCE FOR HIGH DIMENSIONAL AND HIGH FREQUENCY DATA: CONTIGUITY, MATRIX DECOMPOSITIONS, UNCERTAINTY QUANTIFICATION," aims to develop advanced mathematical and statistical methods for extracting information and insights from high-dimensional, high-frequency data.
The research focuses on four key areas: contiguity, matrix decompositions, uncertainty quantification, and the estimation of spot quantities for data occurring in fields such as finance, medicine, and geosciences. The project seeks to enable more efficient estimators and better prediction by leveraging the concept of contiguity, which facilitates statistical analysis of high-frequency data. Additionally, the work will explore time-varying matrix decompositions, including the development of a singular value decomposition (SVD) for high-frequency data, to support factor modeling. The grant will also advance uncertainty quantification techniques to set accurate standard errors and understand trade-offs in longitudinal estimation. This research is expected to have transformational consequences, establishing a new paradigm for high-frequency data analysis.