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Rank correlation under categorical confounding

Author

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  • Jean-François Plante

    (3000 chemin de la Côte-Sainte-Catherine)

Abstract

Rank correlation is invariant to bijective marginal transformations, but it is not immune to confounding. Assuming a categorical confounding variable is observed, the author proposes weighted coefficients of correlation for continuous variables developed within a larger framework based on copulas. While the weighting is clear under the assumption that the dependence is the same within each group implied by the confounder, the author extends the Minimum Averaged Mean Squared Error (MAMSE) weights to borrow strength between groups when the dependence may vary across them. Asymptotic properties of the proposed coefficients are derived and simulations are used to assess their finite sample properties.

Suggested Citation

  • Jean-François Plante, 2017. "Rank correlation under categorical confounding," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-19, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0076-1
    DOI: 10.1186/s40488-017-0076-1
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    References listed on IDEAS

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    1. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    2. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    3. Gijbels, Irène & Veraverbeke, Noël & Omelka, Marel, 2011. "Conditional copulas, association measures and their applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1919-1932, May.
    4. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Noël Veraverbeke & Marek Omelka & Irène Gijbels, 2011. "Estimation of a Conditional Copula and Association Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 766-780, December.
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