## Copula structure analysis based on robust and extreme dependence measures (2006)

Citations: | 2 - 2 self |

### BibTeX

@TECHREPORT{Klüppelberg06copulastructure,

author = {Claudia Klüppelberg and Gabriel Kuhn},

title = {Copula structure analysis based on robust and extreme dependence measures},

institution = {},

year = {2006}

}

### OpenURL

### Abstract

In this paper we extend the standard approach of correlation structure analysis in order to reduce the dimension of highdimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulae a ’correlation-like ’ structure remains but different margins and non-existence of moments are possible. Moreover, elliptical copulae allow also for a ’copula structure analysis ’ of dependence in extremes. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behavior of the statistics can be observed even for a sample of only 100 observations. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach. Our new method yields a considerable dimension reduction also in non-linear models.