Functional generalizations of Hoeffding's covariance lemma and a formula for Kendall's tau

摘要

This note extends Hoeffding's lemma from the covariance between two random variables to that between transformations of random variables, and provides clarification of several existing functional generalizations. In the same spirit as these results, an explicit integral formula of Kendall's tau for general, possibly discontinuous random variables is also determined. (C) 2016 Elsevier B.V. All rights reserved.