Normal correlation coefficient of non-normal variables using piece-wise linear approximation |
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Authors: | Dimitris Kugiumtzis Efthymia Bora-Senta |
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Affiliation: | (1) Department of Psychiatry and Behavioral Sciences, University of Washington, Seattle, WA 98195, USA;(2) Department of Biostatistics, University of Washington, Seattle, WA 98195, USA |
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Abstract: | The correlation coefficient of non-normal variables is expressed as a function of the correlation coefficient of normal variables using piece-wise linear approximation of each univariate transform of normal to anything, and the second order moments of a multiply truncated bivariate normal distribution. For the inverse problem, an algorithm iterates this analytic function in order to assign a normal correlation coefficient to two non-normal variables. The algorithm is applied for the generation of randomized bivariate samples with given correlation coefficient and marginal distributions and used in a randomization test for bivariate nonlinearity. The test correctly does not reject the null hypothesis of linear correlation if the nonlinearity is plausible and due to the sample transform alone. |
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