The collection and analysis of high dimensional data is now of central importance in a wide range of scientific applications, including genomics, bioinformatics, climate studies, and signal processing. There are many new challenges in the analysis of such high dimensional data and there is much demand for the development of new statistical theory and methodology in this field. Although high dimensional data is often analyzed using complex models in many applications, attention is often focused on testing specific hypotheses that are of low dimension. In such cases new statistical theory and methodology relies on the development of new techniques for estimating non-smooth functionals, the topic of this project.
The focus of this research project is to establish a comprehensive methodology for estimating non-smooth functionals and to show how this methodology can be used in the detection and testing of multiple high-dimensional sparse sequences encountered in genomics. The proposed research will provide scientists with new methodologies to analyze such highly complex data. The statistical procedures developed in this project will be implemented in a high-level programming language and made available on the internet with the related research reports so as to allow comparisons with other approaches.
