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Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions

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  • Heinen, Andréas
  • Valdesogo, Alfonso

Abstract

We derive an expression for the Spearman rank correlation of bivariate scale mixtures of normals (SMN) and we show that within this class, for any value of the correlation parameter, the Spearman rank correlation of the normal is the greatest in absolute value. We then provide expressions for the symmetric generalized hyperbolic, the Bessel, and the Laplace distributions. We further derive an expression for the Spearman rank correlation of the Student t distribution in terms of an easily computable one-dimensional integral, and we also consider the special case of the Cauchy. Finally, we show how our results can be used in a rank-based estimation of the parameters of the Student t distribution.

Suggested Citation

  • Heinen, Andréas & Valdesogo, Alfonso, 2020. "Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302311
    DOI: 10.1016/j.jmva.2020.104650
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    References listed on IDEAS

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    1. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
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    3. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Thabane, Lehana & Drekic, Steve, 2003. "Hypothesis testing for the generalized multivariate modified Bessel model," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 360-374, August.
    6. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
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    Cited by:

    1. Cameron Francis Assadian & Francis Assadian, 2023. "Data-Driven Modeling of Appliance Energy Usage," Energies, MDPI, vol. 16(22), pages 1-12, November.
    2. Andréas Heinen & Alfonso Valdesogo, 2022. "The Kendall and Spearman rank correlations of the bivariate skew normal distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1669-1698, December.

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