We suggest correlation coefficients together with rank - and moment based estimators which are simple to compute, have tractable asymptotic distributions, equal the maximum correlation for a class of bivariate Lancester distributions and in particular for the bivariate normal equal the absolute value of the Pearson correlation, while being only slightly smaller than maximum correlation for a variety of bivariate distributions. In a simulation the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably to various competitors, including distance correlation and rank coefficients for functional dependence. Confidence intervals based on the asymptotic distributions and the covariance bootstrap show good finite-sample coverage.

翻译：我们提出了一系列相关系数及其基于秩和矩的估计量，这些估计量计算简单、具有易处理的渐近分布，对于一类二元Lancester分布等于最大相关性，且特别地在二元正态分布下等于Pearson相关系数的绝对值，而对于多种二元分布仅略小于最大相关性。在一项模拟中，基于我们相关性度量的渐近检验和置换检验的统计功效优于多种竞争方法，包括距离相关性和用于函数依赖性的秩系数。基于渐近分布和协方差自助法的置信区间在有限样本下表现出良好的覆盖准确性。