"Bootstrap Methods for Testing Asymptotic Dependence in Multivariate Heavy-Tailed Data"Tiandong WangThe 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 L1 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. We demonstrate this tool using simulated data as well as Finnish rainfall data. In addition, we apply this tool to understand extremal dependence between the sectors of the US and Chinese economies separately and also for analyzing extremal dependence between the US and Chinese economies. |
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