A class of non-parametric statistical manifolds modelled on Sobolev space

DOI10.1007/s41884-019-00024-zzbMath1444.46053arXiv1808.06451OpenAlexW2990687649WikidataQ126757038 ScholiaQ126757038MaRDI QIDQ2279966

Nigel J. Newton

Publication date: 17 December 2019

Published in: Information Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.06451

zbMATH Keywords

Sobolev spaceFokker-Planck equationBanach manifoldFisher-Rao metricnon-parametric statisticslog-Sobolev embedding

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Geometric probability and stochastic geometry (60D05) Filtering in stochastic control theory (93E11) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Applications of functional analysis in probability theory and statistics (46N30) Statistical aspects of information-theoretic topics (62B10) Infinite-dimensional manifolds (46T05)

Related Items (5)

Exponential arcs in the manifold of vector states on a \(\sigma\)-finite von Neumann algebra ⋮ Robust concentration inequalities in maximal exponential models ⋮ A two-parameter family of non-parametric, deformed exponential manifolds ⋮ Estimation with infinite-dimensional exponential family and Fisher divergence ⋮ Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities

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