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Asymptotic behavior of sample mean location for manifolds

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  • Hendriks, Harrie
  • Landsman, Zinoviy

Abstract

We investigate some asymptotic properties of empirical mean location on compact smooth submanifolds of Euclidean space. Thus our results provide the framework for asymptotic least-squares statistics inference regarding mean location in a rather general situation.

Suggested Citation

  • Hendriks, Harrie & Landsman, Zinoviy, 1996. "Asymptotic behavior of sample mean location for manifolds," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 169-178, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:2:p:169-178
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Kanika, & Kumar, Somesh & SenGupta, Ashis, 2015. "A unified approach to decision-theoretic properties of the MLEs for the mean directions of several Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 160-172.
    2. Hendriks, Harrie & Landsman, Zinoviy, 1998. "Mean Location and Sample Mean Location on Manifolds: Asymptotics, Tests, Confidence Regions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 227-243, November.
    3. Stephan Huckemann, 2012. "On the meaning of mean shape: manifold stability, locus and the two sample test," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1227-1259, December.

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