2005/03/01 by Gabriel Frahm, Frahm, Gabriel, Uwe Jaekel +1
Physics and Astronomy · #FOS: Physical sciences #Physics and Society (physics.soc-ph) #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.physics/0503007
arxiv created 2005/03/01 · arxiv updated 2009/12/01
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalization of elliptical distributions and the development of a robust dispersion matrix estimator are motivated by the stylized facts of empirical finance. Random matrix theory is used for analyzing the linear dependence structure of high-dimensional data. It is shown that the Marcenko-Pastur law fails if the sample covariance matrix is considered as a random matrix in the context of elliptically distributed and heavy tailed data. But substituting the sample covariance matrix by the spectral estimator resolves the problem and the Marcenko-Pastur law remains valid.