Post by Christophe Valvason

🎉 Happy to share our new preprint: An Optimal Transportation Approach for Improved Confidence Intervals Co-authored with Eustasio del Barrio and Stefan Andreas Sperlich. I am particularly excited to share this work, as it represents the main contribution of my PhD thesis at Geneva School of Economics and Management - UNIGE. Improving coverage properties in finite samples remains a central challenge in statistical inference. In this work, we investigate how optimal transport can provide a new geometric perspective on this problem. We introduce a statistical framework for constructing nonparametric confidence intervals using optimal transport. In particular, we show that the choice of the source distribution plays a crucial role and can act as a regularization mechanism, leading to improved coverage performances. Our main contributions: • Asymptotic geometric validity. • Finite-sample bounds that explicitly quantify the impact of the source distribution on coverage. • Concentration inequalities for the interval length. In addition, simulations and applications provide empirical evidence of improved coverage properties compared with standard bootstrap methods. 🔗 https://lnkd.in/epBZBEeT Feedback and discussions are welcome. #Statistics #OptimalTransport #Bootstrap