  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 ${\R}^N$, for $N$ sufficiently large.
