Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry

DOI10.1142/S021902579800017XzbMath0921.62004MaRDI QIDQ4213957

Giovanni Pistone, Paolo Gibilisco

Publication date: 27 October 1998

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

vector bundlesOrlicz spacesparallel transportlinear connectionsexponential statistical manifoldsAmari embedding

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Foundations and philosophical topics in statistics (62A01) Global differential geometry (53C99) Applications of functional analysis in probability theory and statistics (46N30)

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Cites Work

• Dual connections and affine geometry
• Fundamental equations for statistical submanifolds with applications to the Bartlett correction
• The relation between information theory and the differential geometry approach to statistics
• Likelihood and observed geometries
• Information geometry in functional spaces of classical and quantum finite statistical systems
• Finite-dimensional algebraic representations of the infinite phylon group
• Defining the curvature of a statistical problem (with applications to second order efficiency)
• Density operators as an arena for differential geometry
• Differential geometry of curved exponential families. Curvatures and information loss
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Monotone metrics on matrix spaces
• Derivative strings, differential strings and semi-holonomic jets
• On a Non-Parametric Analogue of the Information Matrix
• Geometry of canonical correlation on the state space of a quantum system
• Derivative strings: contravariant aspect
• Geometries of quantum states
• An invariant form for the prior probability in estimation problems

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