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A new measure of linear local dependence. (English) Zbl 1039.62052

From the introduction: There are many ways of measuring dependence between two random variables. In a recent book, R. B. Nelsen [An introduction to copulas. Properties and applications. (1999; Zbl 0909.62052)] discusses various measures of dependencies, regarding “correlation coefficient” as a measure of the linear dependence between random variables, and using the term “measure of association” for measures such as Kendall’s tau and Spearman’s rho. Various measures of concordance and their properties are also described in Nelsen’s book, providing relationships between measures of association and dependence of random variables.
This paper provides a description for a new local dependence function based on regression concepts. The measure is symmetric in \(X\) and \(Y\) and its expected value is approximately equal to the Pearson correlation coefficient. We define this new measure in Section 2, where we also discuss its basic properties. In Section 3 we provide examples of several important bivariate distributions. Graphs and tables are collected in Section 4.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62J99 Linear inference, regression

Citations:

Zbl 0909.62052
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