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Automatic differentiation and maximal correlation of order statistics from discrete parents

Author

Listed:
  • Fernando López-Blázquez

    (Universidad de Sevilla)

  • Begoña Salamanca-Miño

    (Universidad de Sevilla)

Abstract

The maximal correlation is an attractive measure of dependence between the components of a random vector, however it presents the difficulty that its calculation is not easy. Here, we consider the case of bivariate vectors which components are order statistics from discrete distributions supported on $$N\ge 2$$ N ≥ 2 points. Except for the case $$N=2$$ N = 2 , the maximal correlation does not have a closed form, so we propose the use of a gradient based optimization method. The gradient vector of the objective function, the correlation coefficient of pairs of order statistics, can be extraordinarily complicated and for that reason an automatic differentiation algorithm is proposed.

Suggested Citation

  • Fernando López-Blázquez & Begoña Salamanca-Miño, 2021. "Automatic differentiation and maximal correlation of order statistics from discrete parents," Computational Statistics, Springer, vol. 36(4), pages 2889-2915, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01103-5
    DOI: 10.1007/s00180-021-01103-5
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    References listed on IDEAS

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    1. Yu, Yaming, 2008. "On the maximal correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1072-1075, July.
    2. Papadatos, Nickos & Xifara, Tatiana, 2013. "A simple method for obtaining the maximal correlation coefficient and related characterizations," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 102-114.
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