A Class of Generalized Correlation Coefficients.

摘要

In this paper we will give a class of generalized correlation coefficients as a measure of association between X(1) and X(2). In particular, we will propose a generalized correlation with desirable optimal properties. For the convenience of presentation, it will be assumed that sigma is positive definite throughout the study. However, if sigma is positive semidefinite the results will remain true with sigma with the limits of ii to -1 replaced by the Moore-Penrose generalized inverse sigma with the limits of ii to + 1, i = 1, 2. For the case of two random variables X sub 1 and X sub 2 (say), i.e., p = q = 1, most frequently used correlations between X sub 1 and X sub 2, such as the Pearson product-moment correlation and the Spearman rank correlation, are invariant with respect to location and scale changes.