A note on positive semi-definiteness of some non-pearsonian correlation matrices
The Pearsonian coefficient of correlation as a measure of association between two variates is highly prone to the deleterious effects of outlier observations (in data). Statisticians have proposed a number of formulas to obtain robust measures of correlation that are considered to be less affected by errors of observation, perturbation or presence of outliers. Spearman’s rho, Blomqvist’s signum, Bradley’s absolute r and Shevlyakov’s median correlation are some of such robust measures of correlation. However, in many applications, correlation matrices that satisfy the criterion of positive semi-definiteness are required. Our investigation finds that while Spearman’s rho, Blomqvist’s signum and Bradley’s absolute r make positive semi-definite correlation matrices, Shevlyakov’s median correlation very often fails to do that. The use of correlation matrices based on Shevlyakov’s formula, therefore, is problematic.
|Date of creation:||14 Jun 2009|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- Mishra, SK, 2007. "The nearest correlation matrix problem: Solution by differential evolution method of global optimization," MPRA Paper 2760, University Library of Munich, Germany, revised 17 Apr 2007.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:15725. 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: (Ekkehart Schlicht)
If references are entirely missing, you can add them using this form.