A Cramér-Rao type lower bound for estimators with values in a manifold
A Cramér-Rao type lower bound for minimum loss unbiased estimators with values in a manifold is derived, and the corresponding notion of efficiency is investigated. A by-product is a generalisation of the concept of covariance of a multivariate statistic to one of a statistic with values in a manifold.
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Article provided by Elsevier in its journal Journal of Multivariate Analysis
Volume (Year): 38 (1991)Handle:
Issue (Month): 2 (August)
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Related researchKeywords: Cramer-Rao inequality minimum variance unbiased estimation unbiased estimators with values in a manifold Hessian Fisher information covariance efficiency Weingarten map exponential family of probability distributions mean location Fisher-von Mises distributions integral manifold
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- Hendriks, Harrie & Landsman, Zinoviy, 1996.
"Asymptotic behavior of sample mean location for manifolds,"
Statistics & Probability Letters,
Elsevier, vol. 26(2), pages 169-178, February.
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