Preferred point geometry and the local differential geometry of the Kullback-Leibler divergence

DOI10.1214/aos/1176325644zbMath0821.62004OpenAlexW2041840807WikidataQ115240735 ScholiaQ115240735MaRDI QIDQ1805567

Mark Salmon, Paul Marriott, Frank Critchley

Publication date: 3 October 1995

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176325644

zbMATH Keywords

statistical manifolddivergence measuresPythagoras' theoremcurvature conditionAmari's alpha-geometryKullback- Leibler divergencenew preferred point geometric structurepreferred point geodesic distance

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Foundations and philosophical topics in statistics (62A01) Statistical aspects of information-theoretic topics (62B10) Local differential geometry (53B99) Methods of local Riemannian geometry (53B21)

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Nonparametric information geometry: from divergence function to referential-representational biduality on statistical manifolds ⋮ Invariant Bayesian estimation on manifolds ⋮ Some notes on preferred point \(\alpha\)-geometry and \(\alpha\)-divergence function ⋮ Preferred point \(\alpha\)-manifold and Amari's \(\alpha\)-connections ⋮ Statistics, yokes and symplectic geometry ⋮ Geometry of the log-likelihood ratio statistic in misspecified models ⋮ Semi-parametric dynamic time series modelling with applications to detecting neural dynamics ⋮ Informative barycentres in statistics ⋮ THE PROPERTIES OF KULLBACK–LEIBLER DIVERGENCE FOR THE UNIT ROOT HYPOTHESIS ⋮ On preferred point geometry in statistics

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