2023/03/31 by Hajo Holzmann, Holzmann, Hajo, Bernhard Klar +1
Computer Science · Mathematics · #62G20 (Secondary) #62H20 (Primary) 62G05 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2303.17872
openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28
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.