Methods of information geometry /
| Main Author: | |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society,
[2000]
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| Series: | Translations of mathematical monographs ;
v. 191. |
| Subjects: | |
| Online Access: | Kostenfrei |
Table of Contents:
- Elementary differential geometry
- Differentiable manifolds
- Tangent vectors and tangent spaces
- Vector fields and tensor fields
- Submanifolds
- Riemannian metrics
- Affine connections and covariant derivatives
- Flatness
- Autoparallel submanifolds
- Projection of connections and embedding curvature
- Riemannian connection
- The geometric structure of statistical models
- Statistical models
- The Fisher metric
- The [alpha]-connection
- Chentsov's theorem and some historical remarks
- The geometry of P (X)
- [alpha]-affine manifolds and [alpha]-families
- Dual connections
- Duality of connections
- Divergences: general contrast functions
- Dually flat spaces
- Canonical divergence
- The dualistic structure of exponential families
- The dualistic structure of [alpha]-affine manifolds and [alpha]-families
- Mutually dual foliations
- A further look at the triangular relation
- Statistical inference and differential geometry
- Estimation based on independent observations
- Exponential families and observed points
- Curved exponential families
- Consistency and first-order efficiency
- Higher-order asymptotic theory of estimation
- Asymptotics of Fisher information
- Higher-order asymptotic theory of tests
- The theory of estimating functions and fiber bundles
- The fiber bundle of local exponential families
- Hilbert bundles and estimating functions
- The geometry of time series and linear systems
- The space of systems and time series.