Robustness and Optimality of Estimation and Testing

该项目致力于通过稳健估计技术的进步来解决现代科学研究中数据污染的挑战。主要目标是开发鲁棒高维估计和鲁棒非参数插值的创新方法，从而能够识别具有不同类型污染的不同数据集的最佳程序。这项研究将对数据科学领域的统计推断产生宝贵的见解。此外，它的影响将超出统计领域，触及基因组学、生物学和社会网络分析等不同学科，在这些学科中，对复杂数据的准确分析至关重要。此外，该项目非常重视教育和社区外展，促进合作和包容性，以释放大数据在科学发现和理解方面的全部潜力。该项目还为研究生提供研究培训机会。该项目解决了在高维和非参数设置中实现最优鲁棒统计推断的挑战。它引入了新的统计方法，满足信息论最优性、计算效率和对污染的鲁棒性的要求。该研究项目涵盖了各种数据污染设置，包括经典的Huber模型和现代的Efron模型。在高维设置中，该项目包含多个比较、可靠的排名和可靠的组同步。在非参数设置中，重点是鲁棒函数插值。该项目认识到存在不同类型的污染，并旨在开发能够适应这些不同场景的最佳稳健程序。此外，该项目强调了创新方法的必要性，以有效处理大型数据集中的污染并提取有意义的见解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.