Robustness of statistical models

10/12/2021

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by   Andrea Loi, et al.

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A statistical structure (g, T) on a smooth manifold M induced by (M̃, g̃, T̃) 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 (M̃, g̃, T̃). Using Nash–Gromov implicit function theorem, we show robustness of the generic statistical structure induced on M by the standard linear statistical structure on ^N, for N sufficiently large.