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.

最大相关性是对随机向量的各个分量之间的相关性的一种有吸引力的度量，但是它带来了难以计算的困难。在这里，我们考虑双变量向量的情况，其分量是\（N \ ge 2 \）个点上支持的离散分布的阶次统计量。除了情况\（N = 2 \）之外，最大相关性没有闭合形式，因此我们建议使用基于梯度的优化方法。目标函数的梯度向量，阶数统计对的相关系数可能会非常复杂，因此提出了一种自动微分算法。