论文标题
新的$ r $估计矩阵的属性
Properties of a new $R$-estimator of shape matrices
论文作者
论文摘要
本文旨在介绍对复杂椭圆形（CES）分布式观测值的新$ r $ r $估计器的主要特性的模拟分析。首先，由Hallin，Oja和Parchaveine提出了现实价值的情况，然后在我们最近的工作中扩展到复杂领域，此$ r $ estimator具有同时的出色属性，同时\ textit {分布性强大}和\ textit {semiparametric效率}。在这里，通过将所得的均方根误差（MSE）与受约束的半磁性cramér-rao绑定（CSCRB）进行比较，研究了此$ r $估计器的不同可能配置的效率。此外，评估了其对离群值的稳健性，并将其与著名的泰勒（Tyler）的估计器之一进行了比较。
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.
