Pearson's correlation coefficient reflects linear dependence in the usual multivariate normal situation, but there are many multivariate distributions for which a high Pearson's indicates a strong non-linear relationship.
You may also want to consider other measures of dependence like Schweizer and Wolff's sigma, or concordance measures like Kendall's tau, Gini's gamma, and Blomqvist's beta, or measures of quadrant dependence. These are discussed in Nelsen's "An Introduction to Copulas." [EMAIL PROTECTED] (Ralph Lorentzen) writes: > > Thank you both. This was very helpful. I was not aware of copulas or > Spearman correlation. I understand now that the standard correlation > coefficient reflects linear dependence whilst one in many cases wants > to check if there is dependence in general. Ideally I would like a > 'correlation coefficient' which, for instance, would be one for the > nonnegative random variables X and X squared. > > Ralph L. -- George MacKenzie Multivariate Models R&D SAS . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
