Mishra, SK (2009): A note on positive semidefiniteness of some nonpearsonian correlation matrices.

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Abstract
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 semidefiniteness are required. Our investigation finds that while Spearman’s rho, Blomqvist’s signum and Bradley’s absolute r make positive semidefinite 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.
Item Type:  MPRA Paper 

Original Title:  A note on positive semidefiniteness of some nonpearsonian correlation matrices 
Language:  English 
Keywords:  Robust correlation; outliers; Spearman’s rho; Blomqvist’s signum; Bradley’s absolute correlation; Shevlyakov’s median correlation; positive semidefinite matrix; fortran 77; computer program 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling 
Item ID:  15725 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  15. Jun 2009 05:51 
Last Modified:  12. Feb 2013 18:05 
References:  Blomqvist, N. (1950) "On a Measure of Dependence between Two Random Variables", Annals of Mathematical Statistics, 21(4): 593600. Bradley, C. (1985) “The Absolute Correlation”, The Mathematical Gazette, 69(447): 1217. Hampel, F. R., Ronchetti, E.M., Rousseeuw, P.J. and W. A. Stahel, W.A. (1986) Robust Statistics: The Approach Based on Influence Functions, Wiley, New York. Mishra, S.K. (2008) “The Nearest Correlation Matrix Problem: Solution by Differential Evolution Method of Global Optimization”, Journal of Quantitative Economics, New Series, 6(1&2): 240262. Shevlyakov, G.L. (1997) “On Robust Estimation of a Correlation Coefficient”, Journal of Mathematical Sciences, 83(3): 434438. Spearman, C. (1904) "The Proof and Measurement of Association between Two Things", American Journal of Psychology, 15: 8893. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/15725 