A van Trees inequality for estimators on manifolds

DOI10.1016/j.jmva.2010.03.007zbMath1352.62043OpenAlexW2021395186MaRDI QIDQ979235

Peter E. Jupp

Publication date: 25 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.jmva.2010.03.007

zbMATH Keywords

tensorHessianCramér-Rao inequalityFisher informationbiasBayes riskproper dispersion model

Mathematics Subject Classification ID

Point estimation (62F10) Bayesian inference (62F15) Statistical aspects of information-theoretic topics (62B10)

Related Items (1)

Lower bounds for invariant statistical models with applications to principal component analysis

Cites Work

• The information matrix, skewness tensor and \(\alpha\)-connections for the general multivariate elliptic distribution
• Information inequalities for the Bayes risk
• Some classes of global Cramér-Rao bounds
• A Cramér-Rao type lower bound for estimators with values in a manifold
• Preferred point geometry and statistical manifolds
• Multivariate dispersion models
• Cramér-Rao revisited
• Applications of the van Trees inequality: A Bayesian Cramér-Rao bound
• Intrinsic analysis of statistical estimation
• Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
• An Extension of the Cramer-Rao Inequality
• A Unified View of the Theory of Directional Statistics, 1975-1988
• Extending Fisher's measure of information
• On Quantum Statistical Inference
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