Rayleigh projection depth
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
Volume (Year): 27 (2012)
Issue (Month): 3 (September)
|Contact details of provider:|| Web page: http://www.springerlink.com/link.asp?id=120306|
|Order Information:||Web: http://link.springer.de/orders.htm|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gao, Yonghong, 2003. "Data depth based on spatial rank," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 217-225, November.
- 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.
When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:27:y:2012:i:3:p:523-530. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.