We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment-based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite-sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets.

翻译：本文提出了一种新型相关系数，该系数在双变量兰开斯特分布族中等于最大相关性，而在多种其他双变量分布中仅略小于最大相关性。然而，与最大相关性不同，我们的相关系数允许基于秩和矩的估计量，这些估计量易于计算且具有易处理的渐近分布。由这些渐近近似和协方差自助法导出的置信区间在有限样本中表现出良好的覆盖率。在模拟中，基于我们所提出的相关度量的独立性渐近检验与置换检验的功效，在与基于距离相关性或秩相关系数（针对函数依赖性）等竞争方法比较时表现更优。此外，对于双变量正态分布，我们的相关系数等于皮尔逊相关性的绝对值，这一特性对实践者具有吸引力，而多种竞争方法并不具备该特性。我们通过对两个真实数据集的应用，展示了所提方法的实践效用。