A note on positive semi-definiteness of some non-pearsonian correlation matrices

Sudhanshu Mishra ()

MPRA Paper from University Library of Munich, Germany

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.

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 (search for similar items in EconPapers)
JEL-codes: C14 C63 (search for similar items in EconPapers)
Date: 2009-06-14
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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