Conformal Geometry of Statistical Manifold with Application to Sequential Estimation

DOI10.1080/07474946.2011.593923zbMath1270.62114arXiv1102.3471OpenAlexW2105997230MaRDI QIDQ3094216

Masayuki Kumon, Kei Takeuchi, Akimichi Takemura

Publication date: 21 October 2011

Published in: Sequential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.3471

zbMATH Keywords

Riemannian metricvon Mises-Fisher distributionaffine connectionsinformation geometryprojective transformationspace of constant curvaturecurved exponential familytotally umbilichyperboloid distribution

Mathematics Subject Classification ID

Statistical aspects of information-theoretic topics (62B10) Sequential estimation (62L12)

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Cites Work

• Unnamed Item
• Unnamed Item
• On the conditions for the existence of ancillary statistics in a curved exponential family
• Studies of information quantities and information geometry of higher order cumulant spaces
• Fundamental equations for statistical submanifolds with applications to the Bartlett correction
• Asymptotic theory of sequential estimation: Differential geometrical approach
• Decomposition and invariance of measures, and statistical transformation models
• Differential-geometrical methods in statistics
• Third order asymptotic efficiency of the sequential maximum likelihood estimation procedure
• On Sequential Maximum Likelihood Estimation for Exponential Families of Stochastic Processes
• On the attainment of the cramer-rao bound in the sequential case
• Ricci-Calculus