A1151
Title: A bridge between statistical approximations, optimal transportation, and information theory
Authors: Elvezio Ronchetti - University of Geneva (Switzerland) [presenting]
Davide La Vecchia - University of Geneva (Switzerland)
Andrej Ilievski - University of Skopje (North Macedonia)
Abstract: Unexplored connections between saddlepoint approximations, measure transportation, and key topics in information theory are presented. A selective review of fundamental results establishes links between Esscher's tilting, a result rooted in information theory and central to saddlepoint approximations, and the solution of the dual Kantorovich problem, a cornerstone of measure transportation theory, via the Legendre transform of the cumulant generating function, also known as the Bahadur half slope. These links are investigated in the framework of M-estimators and quantile regression. The unveiled connections enable saddlepoint approximations to be viewed from different angles, highlighting links to convex analysis through the notion of duality and to differential geometry through the notion of geodesic. Finally, robustness issues of optimal transportation and their connections to penalization methods are addressed.
