Random Matrix Theory and High Dimensional Statistics

High dimensional data are becoming increasingly available from a wide

range of scientific investigations, including genomics, bioinformatics,

engineering, and climate studies. Sound analysis of such datasets poses

many statistical challenges. It calls for new statistical theory and methods

as well as new technical tools. In this collaborative research project, the

investigators will first develop results and technical tools in random matrix

theory and then take a unified approach using the technical tools developed

to study several important problems in high dimensional statistics

as well as applications in signal processing, physics, and mathematics.

The statistical and scientific objectives outlined in this proposal are interdisciplinary

and will establish connections among different fields - random matrix theory, high

dimensional statistics, signal processing, physics, and mathematics. The research

will also provide technical tools as well as methodology, to researchers in other

scientific fields who collect and analyze high dimensional data. These include,

but are not limited to, genomics, biostatistics, and electrical engineering. The procedures and algorithms developed in this project will be implemented and softwares developed will be made freely and publicly available on the web as open source

code along with the associated research reports so as to facilitate the dissemination of knowledge.