Name
Abstract | ||
|---|---|---|
We 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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/978-3-319-25040-3_17 | GEOMETRIC SCIENCE OF INFORMATION, GSI 2015 |
Field | DocType | Volume |
Discrete mathematics,Monotonic function,Tensor,Tensor field,Banach space,Invariant (mathematics),Sample space,Sufficient statistic,Mathematics,Logarithmic derivative | Conference | 9389 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lorenz Schwachhöfer | 1 | 0 | 0.34 |
| Nihat Ay | 2 | 358 | 47.47 |
| Jürgen Jost | 3 | 95 | 12.39 |
| Hông Vân Lê | 4 | 0 | 0.68 |