Bruhacs, Lorand: BCa as Frequentist Inferential Geometry: A Rigorous Curvature Identity and Projective Normal Form

The BCa bootstrap interval can be understood not merely as a higher-order endpoint correction, but as a small piece of frequentist inferential geometry. We isolate a rigorous core for that interpretation. A simple exponential-tilt object built directly from jackknife data recovers the familiar BCa bias and curvature corrections exactly. The classical BCa adjustment is then shown to arise as the unique local transport law within a specific semigroup and factorization class once one imposes a natu