A0269
Title: Lancester correlation: A new dependence measure linked to maximum correlation
Authors: Hajo Holzmann - Philipps-Universität Marburg (Germany) [presenting]
Bernhard Klar - Karlsruhe institute of Technology (Germany)
Abstract: Novel correlation coefficients are suggested that equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than the 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 and permutation tests for independence based on our correlation measures compares favorably to various competitors, including distance correlation and rank coefficients for functional dependence. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners that is not shared by distance correlation, among others. We illustrate the practical usefulness of our methods in applications to two real data sets.
