@techreport{Kluppelberg2006Copula,
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.},
address = {M\"{u}nchen},
author = {Claudia Kl\"{u}ppelberg and Gabriel Kuhn},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {310; copula structure analysis; correlation structure analysis; covariance structure analysis; dimension reduction; elliptical copula; factor analysis; Kendall's tau; tail copula; tail dependence},
language = {eng},
note = {urn:nbn:de:bvb:19-epub-1871-2},
number = {507},
publisher = {Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen},
title = {Copula structure analysis based on robust and extreme dependence measures},
type = {Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universit\"{a}t M\"{u}nchen},
url = {http://hdl.handle.net/10419/31135},
year = {2006}
}
