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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Kugiumtzis, D., Bora-Senta, E. Normal correlation coefficient of non-normal variables using piece-wise linear approximation. Comput Stat 25, 645–662 (2010). https://doi.org/10.1007/s00180-010-0195-3
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DOI: https://doi.org/10.1007/s00180-010-0195-3