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

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

2006-03-22

arxiv.org/abs/physics/0603186v2

Phys.Rev.E74:041129,2006

Physics

Data Analysis, Statistics and Probability

9 pages, 3 figures, references added

Scientific paper

10.1103/PhysRevE.74.041129

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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