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Rayleigh projection depth


  • Yonggang Hu


  • Qiang Li


  • Yong Wang
  • Yi Wu


In this paper, a novel projection-based depth based on the Rayleigh quotient, Rayleigh projection depth (RPD), is proposed. Although, the traditional projection depth (PD) has many good properties, it is indeed not practical due to its difficult computation, especially for the high-dimensional data sets. Defined on the mean and variance of the data sets, the new depth, RPD, can be computed directly by solving a problem of generalized eigenvalue. Meanwhile, we extend the RPD as generalized RPD (GRPD) to make it suitable for the sparse samples with singular covariance matrix. Theoretical results show that RPD is also an ideal statistical depth, though it is less robust than PD. Copyright Springer-Verlag 2012

Suggested Citation

  • Yonggang Hu & Qiang Li & Yong Wang & Yi Wu, 2012. "Rayleigh projection depth," Computational Statistics, Springer, vol. 27(3), pages 523-530, September.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:523-530
    DOI: 10.1007/s00180-011-0273-1

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    References listed on IDEAS

    1. 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.
    2. Gao, Yonghong, 2003. "Data depth based on spatial rank," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 217-225, November.
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    Cited by:

    1. Grünewald, Philipp H. & Cockerill, Timothy T. & Contestabile, Marcello & Pearson, Peter J.G., 2012. "The socio-technical transition of distributed electricity storage into future networks—System value and stakeholder views," Energy Policy, Elsevier, vol. 50(C), pages 449-457.
    2. Marius Bulearca & Catalin Popescu, 2015. "The Strategy For Sustainable Use Of Natural Resources And The Role Of State," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 6, pages 260-264, December.

    More about this item


    Projection depth; Rayleigh quotient; Data depth; Statistical depth; 62H05; 62H30;

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