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Rayleigh projection depth

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  • Yonggang Hu
  • Qiang Li
  • Yong Wang
  • Yi Wu

Abstract

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

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