Robustness of statistical manifolds

Abstract

A statistical structure (g,T) on a smooth manifold M induced by (M˜,g˜,T˜) is said to be robust if there exists an open neighborhood of (g,T) in the fine C∞-topology consisting of statistical structures induced by (M˜,g˜,T˜). Using Nash–Gromov implicit function theorem, we show robustness of the generic statistical structure induced on M by the standard linear statistical structure on RN, for N sufficiently large.