Application of Random Matrix Theory to Structured High-dimensional Data

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The main goal of this application is to utilize spectral analysis techniques for dealing with high-dimensional inferential problems. Techniques of random matrix theory, especially Stieltjes transforms of spectral measures, will be utilized to enhance understanding the effects of dependencies among observations on commonly used statistical procedures in high-dimensional settings. As a key component, investigations on the spectral characteristics of large random matrices with dependencies among both rows and columns will be carried out. In addition, new regularization schemes will be developed that are tuned to the characteristics of the data, including possible non-stationarity of the observations, and make use of the intrinsic parsimonious structures in the data.The proposed application is motivated by problems in a wide range of scientific fields such as wireless communication, spectrometry, genomics, environmental modeling, atmospheric science, brain imaging and econometrics. The emphasis of this proposal is to develop theoretical understanding and practical tools for analyzing complex and large-scale data arising in these disciplines. The research outputs from this project are expected to give wider access among scientists and practitioners in various disciplines to modern statistical tools and concepts for dealing with high-dimensional data. In addition, the tools and ideas developed through this project are likely to contribute towards downstream technologies that require sophisticated real-time data analysis techniques for complex time-varying signals.