From Centrality To Extremity in Multivariate Statistics: Data Depth, Extreme Value Theory and Applications

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Much of multivariate inference and applications evolve around the centrality and/or extremity of the data sets or their underlying distributions. The goals of this proposal are: (i) to develop new nonparametric statistical methodologies for studying the effects of centrality and extremity of data by using data depth and extreme value theory, and (ii) to demonstrate the usefulness of these methodologies in real-life applications, including: using data depth to construct a tractable measure of self-complexity for studying depression and anxiety, detecting performances with extreme risk in the simultaneous monitoring of multiple risk measures, and classifying different genome groups for more effective medical treatments. The research findings would advance the theory underlying each topic and broaden the applicability of statistics to other fields. The lines of investigation are interwoven and are all motivated to build a comprehensive multivariate statistical analysis scheme. This research helps to develop a meaningful self-complexity measure to diagnose patients with psychiatric disorders and provide better health care for such patients. This research also aims to devise an effective threshold system for signaling extreme risks, which should be useful for risk management of rare events, such as in aviation safety or catastrophic events due to climate changes.