Asymptotic Behavior of Sample Mean Direction for Spheres
AbstractIn this note we consider some asymptotic properties of empirical mean direction on spheres. We do not require any symmetry for the underlying density. Thus our results provide the framework for an asymptotic inference regarding mean direction under very weak model assumptions. Mean direction is a specialization of the more general concept of mean location applicable to arbitrary (compact) submanifolds of Euclidean space, to which the methods of this paper could be applied.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 59 (1996)
Issue (Month): 2 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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, vol. 64(6), pages 1227-1259, December.
- 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.
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