Robust-COMET for covariance estimation in convex structures: Algorithm and statistical properties
| Autor: | Arnaud Breloy, Chengfang Ren, Philippe Forster, Bruno Meriaux, Mohammed Nabil El Korso |
|---|---|
| Přispěvatelé: | Sondra, CentraleSupélec, Université Paris-Saclay (COmUE) (SONDRA), ONERA-CentraleSupélec-Université Paris Saclay (COmUE), Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre (UPN), Systèmes et Applications des Technologies de l'Information et de l'Energie (SATIE), École normale supérieure - Cachan (ENS Cachan)-Université Paris-Sud - Paris 11 (UP11)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École normale supérieure - Rennes (ENS Rennes)-Université de Cergy Pontoise (UCP), Université Paris-Seine-Université Paris-Seine-Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Seine-Université Paris-Seine-Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2017 |
| Předmět: |
Covariance matrix
Estimator 020206 networking & telecommunications 02 engineering and technology elliptical distributions Covariance Hermitian matrix Toeplitz matrix Estimation of covariance matrices Robustness (computer science) structured covariance matrix 0202 electrical engineering electronic engineering information engineering Robust covariance estimation 020201 artificial intelligence & image processing [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Elliptical distribution Algorithm Tyler's M-estimator Mathematics |
| Zdroj: | CAMSAP 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017) 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2017), Dec 2017, Curaçao, Netherlands. pp.1-5, ⟨10.1109/CAMSAP.2017.8313081⟩ |
| DOI: | 10.1109/camsap.2017.8313081 |
| Popis: | International audience; This paper deals with structured covariance matrix estimation in a robust statistical framework. Covariance matrices often exhibit a particular structure related to the application of interest and taking this structure into account increases estimation accuracy. Within the framework of robust estimation, the class of circular Complex Elliptically Symmetric (CES) distributions is particularly interesting to handle impulsive and spiky data. Normalized CES random vectors are known to share a common Complex Angular Elliptical distribution. In this context, we propose a Robust Covariance Matrix Estimation Technique (RCOMET) based on Tyler's estimate and COMET criterion for convexly structured matrices. We prove that the proposed estimator is consistent and asymptotically efficient while computationally attractive. Numerical results support the theoretical analysis in a particular application for Hermitian Toeplitz structure. |
| Databáze: | OpenAIRE |
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