Robustness and Optimality of Estimation and Testing

This project is dedicated to tackling the challenge of data contamination in modern scientific studies through the advancement of robust estimation techniques. The primary objective is to develop innovative methods for robust high-dimensional estimation and robust nonparametric interpolation, enabling the identification of optimal procedures for different data sets with varying types of contamination. This research will yield invaluable insights into statistical inference within the realm of data science. Furthermore, its impact will extend beyond the field of statistics, reaching diverse disciplines such as genomics, biology, and social network analysis, where accurate analysis of complex data is of paramount importance. Moreover, this project places a strong emphasis on education and community outreach, fostering collaboration and inclusivity to unleash the full potential of big data for scientific discovery and understanding. The project also provides research training opportunities for graduate students. This project addresses the challenge of achieving optimal robust statistical inference in both high-dimensional and nonparametric settings. It introduces novel statistical methods that satisfy the requirements of information-theoretic optimality, computational efficiency, and robustness to contamination. The research project covers various data contamination settings, including the classical Huber model and the modern Efron's model. In the high-dimensional setting, the project encompasses multiple comparisons, robust ranking, and robust group synchronization. In the nonparametric setting, the focus is on robust function interpolation. This project recognizes the existence of different types of contamination and aims to develop optimal robust procedures that can adapt to these diverse scenarios. Moreover, the project highlights the necessity for innovative methods to effectively handle contamination in large datasets and extract meaningful insights. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.