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Automatic differentiation and maximal correlation of order statistics from discrete parents

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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 \(N\ge 2\) points. Except for the case \(N=2\), 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.

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Acknowledgements

This work was supported by Grant MTM2016-74983-C2 of the Spanish Ministry of Economy and Competitiveness, Grant FQM331 of Junta de Andalucía and the Complex networks meet data science project financed by Fundación BBVA.

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Authors and Affiliations

  1. Department of Statistics & OR, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012, Sevilla, Spain

    Fernando López-Blázquez & Begoña Salamanca-Miño

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  1. Fernando López-Blázquez
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  2. Begoña Salamanca-Miño
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Correspondence to Fernando López-Blázquez.

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López-Blázquez, F., Salamanca-Miño, B. Automatic differentiation and maximal correlation of order statistics from discrete parents. Comput Stat 36, 2889–2915 (2021). https://doi.org/10.1007/s00180-021-01103-5

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  • DOI: https://doi.org/10.1007/s00180-021-01103-5

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