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Eigenvalue Estimation of the Exponentially Windowed Sample Covariance Matrices

In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to f...

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Bibliographic Details
Published in:IEEE transactions on information theory 2016-07, Vol.62 (7), p.4300-4311
Main Authors: Yazdian, Ehsan, Gazor, Saeed, Bastani, Mohammad Hasan, Sharifitabar, Mohsen
Format: Article
Language:English
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Summary:In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size situations. Simulation results show that the proposed estimator outperforms the traditional estimator, significantly.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2562001