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Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2020

Robust Semiparametric Efficient Estimators in Complex Elliptically Symmetric Distributions

Stefano Fortunati
Alexandre Renaux

Résumé

Covariance matrices play a major role in statistics , signal processing and machine learning applications. This paper focuses on the semiparametric covariance/scatter matrix estimation problem in elliptical distributions. The class of elliptical distributions can be seen as a semiparametric model where the finite-dimensional vector of interest is given by the location vector and by the (vectorized) covariance/scatter matrix, while the density generator represents an infinite-dimensional nuisance function. The main aim of this work is then to provide possible estimators of the finite-dimensional parameter vector able to reconcile the two dichotomic concepts of robustness and (semiparametric) efficiency. An R-estimator satisfying these requirements has been recently proposed by Hallin, Oja and Paindaveine for real-valued elliptical data by exploiting the Le Cam's theory of one-step efficient estimators and the rank-based statistics. In this paper, we firstly recall the building blocks underlying the derivation of such real-valued R-estimator, then its extension to complex-valued data is proposed. Moreover, through numerical simulations, its estimation performance and robustness to outliers are investigated in a finite-sample regime.
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Dates et versions

hal-02976900 , version 1 (23-10-2020)

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Stefano Fortunati, Alexandre Renaux, Frédéric Pascal. Robust Semiparametric Efficient Estimators in Complex Elliptically Symmetric Distributions. IEEE Transactions on Signal Processing, 2020, 68, pp.5003-5015. ⟨10.1109/TSP.2020.3019110⟩. ⟨hal-02976900⟩
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