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| HAL : hal-00598826, version 2 |
| arXiv : 1106.1497 |
| DOI : 10.1016/j.jmva.2012.08.006 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Multivariate Analysis 114 (2013) 427-447 |
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| Versions disponibles : | v1 (08-06-2011) | v2 (21-08-2012) |
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| A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices |
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| Walid Hachem 1Philippe Loubaton 2 |
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| (2013) |
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| 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, 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. |
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| 1 : | Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) |
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Télécom ParisTech – CNRS : UMR5141 |
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| 2 : | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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| 3 : | Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) |
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CTTC |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie Mathématiques/Théorie de l'information et codage Informatique/Théorie de l'information et codage Sciences de l'ingénieur/Traitement du signal et de l'image Informatique/Traitement du signal et de l'image |
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| parameter estimation – covariance matrix – large random matrix – MUSIC algorithm |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00598826, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00598826 | |
| oai:hal.archives-ouvertes.fr:hal-00598826 | |
| Contributeur : Jamal Najim | |
| Soumis le : Mardi 21 Août 2012, 14:27:28 | |
| Dernière modification le : Jeudi 21 Février 2013, 22:00:30 | |
