Schwachhöfer, LorenzLorenzSchwachhöferAy, NihatNihatAyJost, JürgenJürgenJostLê, Hông VânHông VânLê2022-11-182022-11-182015-10Lecture Notes in Computer Science 9389 LNIP: 150-158 (2015)http://hdl.handle.net/11420/14098We review the notion of parametrized measure models and tensor fields on them, which encompasses all statistical models considered by Chentsov [6], Amari [3] and Pistone-Sempi [10]. We give a complete description of n-tensor fields that are invariant under sufficient statistics. In the cases n = 2 and n = 3, the only such tensors are the Fisher metric and the Amari-Chentsov tensor. While this has been shown by Chentsov [7] and Campbell [5] in the case of finite measure spaces, our approach allows to generalize these results to the cases of infinite sample spaces and arbitrary n. Furthermore, we give a generalisation of the monotonicity theorem and discuss its consequences.enInformatikMathematikConference Paper10.1007/978-3-319-25040-3_17Other