Characteristics of measures of directional dependence - Monte Carlo studies

by Alexander von Eye and Richard P. DeShon .

Abstract: In the context of linear models, the response variable will always have less skew than the explanatory variable. Based on this result, one can use third and fourth order moments, and information concerning the deviation of variables from normality, to ascertain which of two variables is the response and which is the explanatory variable. In this article, the ratio of two skewness measures, the ratio of two kurtosis measures, and one omnibus test of deviation from normality are examined. Results from simulation studies show that all three measures (1) are sensitive to various data distributions, (2) sample size, and (3) a simple correlation structure. The ratio of two kurtosis measures is sensitive in particular to the correlation structure. It is concluded that (1) decisions about directional dependence can be based on various types of deviation from normality, (2) measures that respond to deviations based on skewness and kurtosis have characteristics that make them prime candidates for determining directional dependence, and (3) each of the measures proposed thus far is sensitive to either specific or omnibus deviations from normality.

Key Words: directional dependence, simulation, skewness, kurtosis, normality

Alexander von Eye,
Richard P. DeShon,

Editor: Richard G. Graf,

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