Spectral properties of empirical covariance matrices for data with power-law tails

Zdzislaw Burda; Andrzej Goerlich; Bartlomiej Waclaw

doi:10.1103/physreve.74.041129

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Spectral properties of empirical covariance matrices for data with power-law tails

Zdzislaw Burda·Andrzej Goerlich·Bartlomiej Waclaw

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Abstract

We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the system. The method is applicable to a class of random matrices with radial measures including those with heavy (power-law) tails in the probability distribution. As an example we apply it to a multivariate Student distribution.

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Zdzislaw Burda, Andrzej Goerlich, Bartlomiej Waclaw. 2006-04-20. Spectral properties of empirical covariance matrices for data with power-law tails. https://doi.org/10.1103/physreve.74.041129

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