Dimension reduction based on extreme dependence

We introduce a dimension reduction technique based on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a fairly general model for the copula. We assume an elliptical copula to describe the extreme dependence structure, which preserves a ’correlation-like’ structure in the extremes. Based on the tail dependence function we estimate the copula correlation matrix, which is then analysed through classical dimension reduction techniques. After introducing the new concepts and deriving some theoretical results we observe in a simulation study the performance of the estimator. Finally, we test our method on real financial data and explain differences between our copula based approach and the classical approach.