A note on fourth moment-based direction dependence measures when regression errors are non normal

Wolfgang Wiedermann

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 21, 5255-5264

Abstract: Measures of direction dependence enable researchers to determine the directionality of linear effects in bivariate data. Existing fourth moment-based approaches assume that regression errors are at least mesokurtic. Direction dependence measures based on the co-kurtosis of variables are proposed that relax this assumption. Simulations suggest that co-kurtosis-based measures perform equally well as existing kurtosis-based methods when distributional assumptions of the latter are fulfilled. However, kurtosis-based approaches are sensitive to platy- or leptokurtic errors, while co-kurtosis-based measures protect Type I error and power rates. Data requirements necessary for causal inference and recommendations for selecting proper direction dependence measures are discussed.

Date: 2018
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DOI: 10.1080/03610926.2017.1388403

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