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Normal correlation coefficient of non-normal variables using piece-wise linear approximation

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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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Authors and Affiliations

  1. Department of Mathematical, Physical and Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Dimitris Kugiumtzis

  2. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Efthymia Bora-Senta

Authors
  1. Dimitris Kugiumtzis
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  2. Efthymia Bora-Senta
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Correspondence to Dimitris Kugiumtzis.

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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

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