A subspace estimator for fixed rank perturbations of large random matrices

Walid Hachem, Philippe Loubaton, Xavier Mestre, Jamal Najim and Pascal Vallet

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 427-447

Abstract: This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series dimension and the observation window grow to infinity at the same pace. In the area of large random matrix theory, recent contributions studied the behavior of the extreme eigenvalues of a random matrix and their associated eigenspaces when this matrix is subject to a fixed-rank perturbation. The present work is concerned with the situation where the parameters to be estimated determine the eigenspace structure of a certain fixed-rank perturbation of the empirical covariance matrix. An estimation algorithm in the spirit of the well-known MUSIC algorithm for parameter estimation is developed. It relies on an approach recently developed by Benaych-Georges and Nadakuditi (2011) [8,9], relating the eigenspaces of extreme eigenvalues of the empirical covariance matrix with eigenspaces of the perturbation matrix. First and second order analyses of the new algorithm are performed.

Keywords: Large random matrix theory; MUSIC algorithm; Extreme eigenvalues; Finite rank perturbations (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.jmva.2012.08.006

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