Signal and Noise in Correlation Matrix

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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17 pages, 3 figures, corrected typos, revtex style changed to elsart

Scientific paper

10.1016/j.physa.2004.05.048

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.

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