Skewness and the linear discriminant function
Fisher’s linear discriminant function might be difficult to estimate, when data come from a semiparametric, finite mixture model. We propose an estimator based on the singular value decomposition of the third standardized cumulant. The estimator is consistent when sampling from a mixture of two symmetric, homoscedastic components with finite third moments and different weights. We also evaluate its performance and compare it with another estimator, which uses the eigenvectors of a kurtosis matrix.
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): 83 (2013)
Issue (Month): 1 ()
|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.:
- Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(2), pages 389-401, June.
- Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
- Pena D. & Prieto F.J., 2001. "Cluster Identification Using Projections," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1433-1445, December.
- Posse, Christian, 1995. "Projection pursuit exploratory data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 669-687, December.
- Peña, Daniel & Prieto, Francisco J. & Viladomat, Júlia, 2010. "Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1995-2007, October.
- Kollo, Tõnu, 2008. "Multivariate skewness and kurtosis measures with an application in ICA," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2328-2338, November.
- Peña, Daniel & Prieto, Francisco J., 2000. "The kurtosis coefficient and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 257-261, September.
- T. P. Hettmansperger & Hoben Thomas, 2000. "Almost nonparametric inference for repeated measures in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 811-825.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:93-99. 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 references are entirely missing, you can add them using this form.