A Cramér-Rao type lower bound for estimators with values in a manifold

DOI10.1016/0047-259X(91)90044-3zbMath0753.62032OpenAlexW2134656181MaRDI QIDQ1175669

Harrie Hendricks

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0047-259x(91)90044-3

zbMATH Keywords

exponential familiesminimum variance unbiased estimationefficiencyHessianFisher informationexponential familyintegral manifoldinformation inequalityWeingarten mapmean locationFisher-von Mises distributionsconcept of covarianceCramer-Rao type lower boboundmanifold-valued estimatorsminimum loss unbiased estimators

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of homogeneous manifolds (53C30)

Related Items (9)

Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements ⋮ Asymptotic behavior of sample mean location for manifolds ⋮ Intrinsic sample mean in the space of planar shapes ⋮ Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds ⋮ Semiparametric estimation of shifts on compact Lie groups for image registration ⋮ The admissibility of the empirical mean location for the matrix von Mises-Fisher family ⋮ A van Trees inequality for estimators on manifolds ⋮ Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions ⋮ A new extrinsic sample mean in the shape space with applications to the boundaries of anatomical structures

Cites Work

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• Morse Theory. (AM-51)
• Linear Statistical Inference and its Applications
• Dispersion on a Sphere
• On the attainment of the Cramer-Rao lower bound

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