Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data

The ability to unambiguously classify the asymptotic dependence structure of multivariate data is often beyond the capability of graphical, exploratory tools. We present a rigorous and practical classification framework that leads to categorizing dependence structures into four main cases: (i) asymptotic independence, (ii) strong dependence, (iii) full dependence, and (iv) weak dependence. For bivariate non-negative heavy tailed data, switch to polar coordinates with the L 1 norm and these four cases are characterized respectively by the concentration of the limit angular measure on (i) {0, 1}, (ii) a proper subset of [0, 1], (iii) a single point, and (iv) the whole interval [0, 1]. Based on bootstrap methods we arrive at a comprehensive and theoretically justified classification tool. Here we demonstrate this tool using simulated data as well as the Finnish rainfall data.