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Activity Number:
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107
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Type:
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Contributed
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Date/Time:
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Monday, July 30, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #309410 |
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Title:
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Statistical Eigen-Inference from Large Wishart Matrices
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Author(s):
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Raj Rao*+
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Companies:
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Massachusetts Institute of Technology
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Address:
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195 Binney Street Apt 2227, Cambridge, MA, 02142,
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Keywords:
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random matrices ; eigen-inference ; Wishart matrices
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Abstract:
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The asymptotic behavior of the eigenvalues of a sample covariance matrix is described when the observations are from a zero mean multivariate (real or complex) normal distribution whose covariance matrix has population eigenvalues of arbitrary multiplicity. In particular, the asymptotic normality of the fluctuation in the trace of powers of the sample covariance matrix from the limiting quantities is shown. Concrete algorithms for analytically computing the limiting quantities and the covariance of the fluctuations are presented. Tests of hypotheses for the population eigenvalues are developed and a technique for inferring the population eigenvalues is proposed that exploits this asymptotic normality of the trace of powers of the sample covariance matrix. Numerical simulations demonstrate the robustness of the proposed techniques in techniques in high-dimensional settings.
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