Dependence Measures: Rank Correlations

This lecture covers rank correlations and tail dependence measures, focusing on linear correlation, rank correlation, and tail dependence coefficients. Rank correlations are invariant under linear transformations and provide a copula-based parametrization. The lecture also discusses fallacies related to correlation statements and the properties of rank correlations. Additionally, it explores Spearman's rho and Kendall's tau as measures of concordance, along with examples of bivariate Archimedean copulas and Laplace-Stieltjes transforms. The fitting of copulas to data is addressed, emphasizing the use of sample rank correlations and maximum likelihood estimation.