Advances in Game-Theoretic Statistics: e-Values for Testing, Estimation and Change Detection

This project advances a new framework for statistical inference called game-theoretic statistics, which uses “testing by betting” to analyze uncertainty in data. Modern scientific and technological systems increasingly rely on data that arrive continuously over time; such areas include medicine, finance, cybersecurity, and online platforms. Traditional statistical methods are often not designed for such continuously monitored settings, especially when models are uncertain or incomplete. This project develops mathematical foundations and practical tools that allow reliable decision-making under these challenging conditions. By creating methods that remain valid under continuous monitoring and flexible modeling assumptions, the research seeks to improve the reliability, transparency, and adaptability of data-driven scientific conclusions. The project also strengthens connections among statistics, machine learning, game theory, and mathematical finance, thereby advancing multiple research communities simultaneously. Broader impacts include training graduate students and postdoctoral researchers, organizing international workshops and educational activities, and disseminating ideas to academic, industrial, and public audiences. These advances support the progress of science and contribute to national interests in health, economic innovation, and secure data-driven systems. The project develops the mathematical and algorithmic foundations of e-values and e-processes, central tools in game-theoretic statistics that enable sequential and nonparametric statistical inference through betting-based methods. The research focuses on three interconnected thrusts: hypothesis testing, estimation, and changepoint detection. In hypothesis testing, the project studies admissibility, optimality, and multiple testing procedures for nonsequential and sequential settings. In estimation, the project develops general methodologies for constructing betting-based confidence sets and confidence sequences for scalar, vector, and matrix parameters in both nonasymptotic and asymptotic regimes. In changepoint detection, the project investigates universal and asymptotically optimal methods for detecting distributional changes in single-stream and multi-stream data. The work emphasizes methods that are inherently sequential, model-flexible, and compatible with continuous updating while integrating frequentist and Bayesian perspectives. The resulting theory and algorithms are expected to deepen understanding of statistical inference under uncertainty and establish new connections with online learning, mathematical finance, and game-theoretic probability. 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.