Congruent families and invariant tensors

Publikationstyp
Book Part
Date Issued
2018
Sprache
English
Author(s)
Schwachhöfer, Lorenz  
Ay, Nihat  
Jost, Jürgen  
Vân Lê, Hông  
TORE-URI
http://hdl.handle.net/11420/10352
First published in
Springer proceedings in mathematics & statistics  
Number in series
252
Start Page
157
End Page
187
Citation
Springer Proceedings in Mathematics and Statistics 252: 157-187 (2018)
Publisher DOI
10.1007/978-3-319-97798-0_6
Scopus ID
2-s2.0-85056330084
Publisher
Springer
ISBN
978-3-319-97798-0
978-3-319-97797-3
A 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]).
Subjects
Chentsov’s theorem
Congruent Markov kernel
Statistical model
Sufficient statistic
DDC Class
600: Technology