An infinite-dimensional statistical manifold modelled on Hilbert space

DOI10.1016/j.jfa.2012.06.007zbMath1257.46044OpenAlexW1963853631MaRDI QIDQ452364

Nigel J. Newton

Publication date: 21 September 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2012.06.007

zbMATH Keywords

Hilbert manifoldinformation theoryBayesian estimationinformation geometryFisher metricFenchel-Legendre transform

Mathematics Subject Classification ID

Foundations and philosophical topics in statistics (62A01) Applications of functional analysis in probability theory and statistics (46N30) Infinite-dimensional manifolds (46T05)

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Cites Work

• Exponential statistical manifold
• Dual connections in nonparametric classical information geometry
• The exponential statistical manifold: mean parameters, orthogonality and space transformations
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Dualistic Riemannian Manifold Structure Induced from Convex Functions
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• A Variational Approach to Nonlinear Estimation
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