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Connecting pairwise geodesic spheres by depth: DCOPS

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  • Fraiman, Ricardo
  • Gamboa, Fabrice
  • Moreno, Leonardo

Abstract

We extend the classical notion of spherical depth for data in Rk to the case of data on a Riemannian manifold. We show that this notion has several desirable properties. The uniform consistency and limiting distribution of an empirical analogue of this depth function are studied. Consistency is also shown for functional data. Various illustrations involving Riemannian manifold data are included.

Suggested Citation

  • Fraiman, Ricardo & Gamboa, Fabrice & Moreno, Leonardo, 2019. "Connecting pairwise geodesic spheres by depth: DCOPS," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 81-94.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:81-94
    DOI: 10.1016/j.jmva.2018.08.008
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    References listed on IDEAS

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    1. Lizhen Lin & Brian St. Thomas & Hongtu Zhu & David B. Dunson, 2017. "Extrinsic Local Regression on Manifold-Valued Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1261-1273, July.
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    3. Zhu, Hongtu & Chen, Yasheng & Ibrahim, Joseph G. & Li, Yimei & Hall, Colin & Lin, Weili, 2009. "Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1203-1212.
    4. Carrizosa, Emilio, 1996. "A Characterization of Halfspace Depth," Journal of Multivariate Analysis, Elsevier, vol. 58(1), pages 21-26, July.
    5. Zhenyu Liu & Reza Modarres, 2011. "Lens data depth and median," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1063-1074.
    6. Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
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    Cited by:

    1. S. Barahona & P. Centella & X. Gual-Arnau & M. V. Ibáñez & A. Simó, 2020. "Supervised classification of geometrical objects by integrating currents and functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 637-660, September.
    2. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.

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