Warped Riemannian metrics for location-scale models

@article{Said2019WarpedRM,
  title={Warped Riemannian metrics for location-scale models},
  author={S. Said and L. Bombrun and Y. Berthoumieu},
  journal={arXiv: Statistics Theory},
  year={2019},
  pages={251-296}
}
The present contribution shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the starting point is a new theorem, which states that the Rao–Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool… Expand
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