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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