High breakdown estimators for principal components: the projection-pursuit approach revisited
Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with maximal variance, and their approach consists of replacing this variance by a robust scale measure. Li and Chen showed that this estimator is consistent, qualitative robust and inherits the breakdown point of the robust scale estimator. We complete their study by deriving the influence function of the estimators for the eigenvectors, eigenvalues and the associated dispersion matrix. Corresponding Gaussian efficiencies are presented as well. Asymptotic normality of the estimators has been treated in a paper of Cui et al. (Biometrika 90 (2003) 953), complementing the results of this paper. Furthermore, a simple explicit version of the projection-pursuit based estimator is proposed and shown to be fast to compute, orthogonally equivariant, and having the maximal finite-sample breakdown point property. We will illustrate the method with a real data example.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 95 (2005)
Issue (Month): 1 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
- N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-73, June.
- Croux, Christophe, 1994. "Efficient high-breakdown M-estimators of scale," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 371-379, April.
- Hengjian Cui, 2003. "Asymptotic distributions of principal components based on robust dispersions," Biometrika, Biometrika Trust, vol. 90(4), pages 953-966, December.
- Graciela Boente, 2002. "Influence functions and outlier detection under the common principal components model: A robust approach," Biometrika, Biometrika Trust, vol. 89(4), pages 861-875, December.
- Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
- Abul Naga, Ramses & Antille, Gerard, 1990. "Stability of robust and non-robust principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 10(2), pages 169-174, October.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:95:y:2005:i:1:p:206-226. 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: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.