Schwachhöfer, LorenzLorenzSchwachhöferAy, NihatNihatAyJost, JürgenJürgenJostVân Lê, HôngHôngVân Lê2021-09-162021-09-162018Springer Proceedings in Mathematics and Statistics 252: 157-187 (2018)http://hdl.handle.net/11420/10352A classical result of Chentsov states that – up to constant multiples – the only 2-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant 3-tensor field is the Amari–Chentsov tensor. We generalize this result for arbitrary degree n, showing that any family of n-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in Ay, Jost, Lê, Schwachhöfer (Bernoulli, 24:1692–1725, 2018, [4]).enChentsov’s theoremCongruent Markov kernelStatistical modelSufficient statisticBook Part10.1007/978-3-319-97798-0_6Other