In information geometry, Chentsov's theorem states that the Fisher information metric is, up to rescaling, the unique Riemannian metric on a statistical manifold that is invariant under sufficient statistics.
The theorem is named after mathematician Nikolai Chentsov, who proved it in his 1981 paper.
See also
References
- N. N. ÃÂencov (1981), Statistical Decision Rules and Optimal Inference, Translations of mathematical monographs; v. 53, American Mathematical Society, http://www.ams.org/books/mmono/053/
- Shun'ichi Amari, Hiroshi Nagaoka (2000) Methods of information geometry, Translations of mathematical monographs; v. 191, American Mathematical Society, http://www.ams.org/books/mmono/191/ (Theorem 2.6)