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Copula Structure Analysis

Claudia Klüppelberg and Gabriel Kuhn
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 71, No. 3 (Jun., 2009), pp. 737-753
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/40247598
Page Count: 17
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Copula Structure Analysis
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Abstract

We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional 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 copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copulabased approach and the classical approach. Our new method yields a considerable reduction in dimension in non-linear models also.

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