In article <[EMAIL PROTECTED]>, Ralph Lorentzen <[EMAIL PROTECTED]> wrote: >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.
One can define the maximal correlation as the least upper bound of the product-moment correlation between two increasing functions of the random variables. The problem is that this is 1 in many cases where there is little dependence; for example, if there is a largest possible value for each of the random variables which can only occur for one if and only if it does for the other, even if this happens with small probability, and otherwise the random variables are independent. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
