Functional data analysis, which deals with a sample of functions or curves, plays an important role in modern data analysis. Nowadays in the era of "Big Data", multidimensional and multivariate functional data are becoming increasingly common, especially in biological, medical, and engineering applications. There are significant challenges posed by the very large dimension and complex structure of these data. The proposed research will substantially narrow the gap between the increasing demand for handling such data in practice, and the insufficient development of statistical methods and computational tools. This research has applications to neuroscience, climate science, and engineering. It will provide scientists, engineers, and doctors with tools to help understand problems in their area, and enhance interdisciplinary collaborations.

This project offers a comprehensive research plan to advance the understanding and applicability of multidimensional and multivariate functional data. The research will focus on the following three sub-projects: (1) Develop data-adaptive and interpretable representation of the covariance function for multidimensional functional data, (2) Develop a novel model-free procedure to detect dependency between components of multivariate functional data, and (3) Address the modeling and prediction of multivariate functional time series. The resulting methods will be applied to neuroimaging and climate data. The integration of these three sub-projects will foster creative directions and strategies for multidimensional and multivariate functional data.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1832046
Program Officer
Gabor Szekely
Project Start
Project End
Budget Start
2017-08-01
Budget End
2020-06-30
Support Year
Fiscal Year
2018
Total Cost
$76,912
Indirect Cost
Name
George Washington University
Department
Type
DUNS #
City
Washington
State
DC
Country
United States
Zip Code
20052