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

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  • Hendriks, Harrie

Abstract

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.

Suggested Citation

  • Hendriks, Harrie, 1991. "A Cramér-Rao type lower bound for estimators with values in a manifold," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 245-261, August.
    • Handle: RePEc:eee:jmvana:v:38:y:1991:i:2:p:245-261
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    Cited by:

    1. Hendriks, Harrie, 2005. "The admissibility of the empirical mean location for the matrix von Mises-Fisher family," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 454-464, February.
    2. Steven E. Pav, 2014. "Bounds on Portfolio Quality," Papers 1409.5936, arXiv.org.
    3. 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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