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A note on positive semi-definiteness of some non-pearsonian 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 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.

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  • Mishra, SK, 2009. "A note on positive semi-definiteness of some non-pearsonian correlation matrices," MPRA Paper 15725, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15725
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    File URL: https://mpra.ub.uni-muenchen.de/15725/1/MPRA_paper_15725.pdf
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    1. 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.
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    Cited by:

    1. Nayak, Purusottam & Mishra, SK, 2014. "A state level analysis of the status of social sector in India," MPRA Paper 58144, University Library of Munich, Germany.

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      Keywords

      Robust correlation; outliers; Spearman’s rho; Blomqvist’s signum; Bradley’s absolute correlation; Shevlyakov’s median correlation; positive semi-definite matrix; fortran 77; computer program;
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      JEL classification:

      • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
      • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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