The multivariate Piecing-Together approach revisited

[摘要] The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al. (in press) [2]: the upper tail of a given copula C is cut off and replaced by a multivariate GPD-copula in a continuous manner, yielding a new copula called a PT-copula. Then each margin of this PT-copula is transformed by a given univariate distribution function. This provides a multivariate distribution function with prescribed margins, whose copula is a GPD-copula that coincides in its central part with C. In addition to Aulbach et al. (in press) [2], we achieve in the present paper an exact representation of the PT-copula's upper tail, giving further insight into the multivariate PT approach. A variant based on the empirical copula is also added. Furthermore our findings enable us to establish a functional PT version as well. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-09-01

[效力级别]  Proceedings Paper

[关键词] Copula;Copula process;D-norm;Domain of multivariate attraction;Empirical copula;GPD-copula;Max-stable process;Multivariate extreme value distribution;Multivariate generalized Pareto distribution;Peaks-over-threshold;Piecing-Together approach