Lancester correlation -- a new dependence measure linked to maximum correlation

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.