A statistical manifold modeled on Orlicz spaces using Kaniadakis \(\kappa\)-exponential models

DOI10.1016/j.jmaa.2015.05.065zbMath1373.46022OpenAlexW365933810MaRDI QIDQ491823

Juan C. Arango Parra, Héctor R. Quiceno Echavarría

Publication date: 19 August 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.05.065

zbMATH Keywords

Orlicz spacedifferential geometryinformation theorystatistical manifold\(\kappa\)-exponential family

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Global differential geometry (53C99)

Cites Work

• A construction of a nonparametric quantum information manifold
• \(\kappa \)-exponential models from the geometrical viewpoint
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• Differential-geometrical methods in statistics
• Quantum Orlicz Spaces in Information Geometry
• An invariant form for the prior probability in estimation problems
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