A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergen...
- Autores:
-
Quiceno, H. R.
Loaiza, Gabriel
- Tipo de recurso:
- Fecha de publicación:
- 2013
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/4401
- Acceso en línea:
- http://hdl.handle.net/10784/4401
- Palabra clave:
- q-Exponential
Banach Manifold
Geometry
- Rights
- License
- Acceso restringido
| Summary: | For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold. |
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