Abstract
The tail-dependence compatibility problem is introduced. It raises the question whether a given $d\times d$-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a $d$-dimensional random vector. The problem is studied together with Bernoulli-compatible matrices, that is, matrices which are expectations of outer products of random vectors with Bernoulli margins. We show that a square matrix with diagonal entries being 1 is a tail-dependence matrix if and only if it is a Bernoulli-compatible matrix multiplied by a constant. We introduce new copula models to construct tail-dependence matrices, including commonly used matrices in statistics.
Citation
Paul Embrechts. Marius Hofert. Ruodu Wang. "Bernoulli and tail-dependence compatibility." Ann. Appl. Probab. 26 (3) 1636 - 1658, June 2016. https://doi.org/10.1214/15-AAP1128
Information