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In this paper, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The consistency is then extended to the case where the aggregated matrix of time samples is corrupted by a rank one (or more generally, low rank) matrix. As an application...
In this paper, performance results of two types of Toeplitz covariance matrix estimators are provided. Concentration inequalities for the spectral norm for both estimators have been derived showing exponential convergence of the error to zero. It is shown that the same rates of convergence are obtained in the case where the aggregated matrix of time samples is corrupted by a rank one matrix. As an...
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