Keywords: restricted inference, dimension reduction, information geometry, minimum distance test
It is well-known that Fisher information induces a Riemannian structure on a statistical manifold. We use this fact to derive information tests that exploit the Riemannian geometry of dimension-restricted statistical submanifolds. Information tests are locally asymptotically equivalent to various classical tests; however, despite their conceptual appeal, they are of limited practical value. We propose discrete approximations of information tests and demonstrate their effectiveness on several examples.