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arXiv · 2002.11967

Properties of a new $R$-estimator of shape matrices

Stefano Fortunati·Alexandre Renaux·Frédéric Pascal
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Abstract

This paper aims at presenting a simulative analysis of the main properties of a new $R$-estimator of shape matrices in Complex Elliptically Symmetric (CES) distributed observations. First proposed by Hallin, Oja and Paindaveine for the real-valued case and then extended to the complex field in our recent work, this $R$-estimator has the remarkable property to be, at the same time, \textit{distributionally robust} and \textit{semiparametric efficient}. Here, the efficiency of different possible configurations of this $R$-estimator are investigated by comparing the resulting Mean Square Error (MSE) with the Constrained Semiparametric Cramér-Rao Bound (CSCRB). Moreover, its robustness to outliers is assessed and compared with the one of the celebrated Tyler's estimator.

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Stefano Fortunati, Alexandre Renaux, Frédéric Pascal. 2020-06-21. Properties of a new $R$-estimator of shape matrices. https://arxiv.org/abs/2002.11967

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