Lancaster相关——一种与最大相关相联系的新依赖度量
Lancaster correlation -- a new dependence measure linked to maximum correlation
AI总结：
本文提出Lancaster相关系数，对一类二元Lancaster分布等于最大相关，且支持简单可计算的秩与矩估计量，在独立性检验功效上优于距离相关等方法，并在二元正态情形下等于Pearson相关绝对值。
摘要：
我们提出新的相关系数，这些系数对于一类二元Lancaster分布等于最大相关，而对于多种其他二元分布仅略小于最大相关。然而，与最大相关不同，我们的相关系数允许基于秩和矩的估计量，这些估计量计算简单且具有可处理的渐近分布。由这些渐近近似和协方差bootstrap得到的置信区间表现出良好的有限样本覆盖率。在模拟中，基于我们的相关度量的渐近检验以及置换独立性检验的功效，与基于距离相关或秩系数的函数依赖竞争方法等相比具有优势。此外，对于二元正态分布，我们的相关系数等于Pearson相关的绝对值，这一对实践者有吸引力的特性是许多竞争方法所不具备的。我们通过应用于两个真实数据集展示了我们方法的实际效用。
英文摘要：
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.
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