Robustness of statistical models

Abstract

A statistical structure $(g,T)$ on a smooth manifold $M$ induced by $(\tilde{M},\tilde{g},\tilde{T})$ is said to be {\em robust} if there exists an open neighborhood of $(g,T)$ in the fine $C^{\infty }$-topology consisting of statistical structures induced by $(\tilde{M},\tilde{g},\tilde{T})$. Using Nash--Gromov implicit function theorem, we show robustness of the generic statistical structure induced on $M$ by the standard linear statistical structure on ${\mathbb{R}}^N$, for $N$ sufficiently large.

8 pages