This talk is based on joint work with J. Dueck, D. Edelmann (Heidelberg University) and T. Gneiting (Heidelberg Institute for Theoretical Studies). Szekely, Rizzo and Bakirov (2007) and Szekely and Rizzo (2009), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets of random variables. We describe in this talk an affinely invariant version of the distance correlation and an empirical version of that distance correlation, and we establish the consistency of the empirical version. In the case of sub-vectors of a multivariate normally distributed random vector, we provide exact expressions for the distance correlation in both finite-dimensional and asymptotic settings. We illustrate these results by considering time series of wind vectors at the Stateline wind energy center in the states of Oregon and Washington.
