dorsal/arxiv
View SchemaRandom matrix theory and robust covariance matrix estimation for financial data
| Authors | Gabriel Frahm, Uwe Jaekel |
|---|---|
| Categories | |
| ArXiv ID | physics/0503007 |
| URL | https://arxiv.org/abs/physics/0503007 |
Abstract
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.
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"abstract": "The traditional class of elliptical distributions is extended to allow for\nasymmetries. A completely robust dispersion matrix estimator (the `spectral\nestimator\u0027) for the new class of `generalized elliptical distributions\u0027 is\npresented. It is shown that the spectral estimator corresponds to an\nM-estimator proposed by Tyler (1983) in the context of elliptical\ndistributions. Both the generalization of elliptical distributions and the\ndevelopment of a robust dispersion matrix estimator are motivated by the\nstylized facts of empirical finance. Random matrix theory is used for analyzing\nthe linear dependence structure of high-dimensional data. It is shown that the\nMarcenko-Pastur law fails if the sample covariance matrix is considered as a\nrandom matrix in the context of elliptically distributed and heavy tailed data.\nBut substituting the sample covariance matrix by the spectral estimator\nresolves the problem and the Marcenko-Pastur law remains valid.",
"arxiv_id": "physics/0503007",
"authors": [
"Gabriel Frahm",
"Uwe Jaekel"
],
"categories": [
"physics.soc-ph"
],
"title": "Random matrix theory and robust covariance matrix estimation for financial data",
"url": "https://arxiv.org/abs/physics/0503007"
},
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