The multivariate Piecing-Together approach revisited

Details The multivariate Piecing-Together approach revisited The multivariate Piecing-Together approach revisited

2011-08-03

arxiv.org/abs/1108.0920v4

Mathematics

Probability

12 pages, 1 figure. To appear in the Journal of Multivariate Analysis

Scientific paper

10.1016/j.jmva.2012.02.002

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. (2012a): 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. (2012a), 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.

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