The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints. This joint estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an infinite-dimensional nuisance parameter. In the first part of the paper, a computationally efficient and memory saving implementation of the robust and semiparmaetric efficient R-estimator for shape matrices is derived. Building upon this result, in the second part, a joint estimator, relying on the Tyler’s M-estimator of location and on the R-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cramér-Rao Bound (SCRB).

从理论和计算的角度研究了一组独立且相同的复椭圆对称 (CES) 分布式观测的位置向量和形状矩阵的联合估计。这个联合估计问题是在半参数模型的原始上下文中构建的，允许我们将（通常未知的）密度生成器作为一个无限维的麻烦参数来处理。在论文的第一部分中，推导出了形状矩阵的鲁棒和半参数高效R估计器的计算效率和内存节省实现。在此结果的基础上，在第二部分中，联合估计器依赖于 Tyler 的M位置估计器和R提出了形状矩阵的估计器，并将其均方误差 (MSE) 性能与半参数 Cramér-Rao Bound (SCRB) 进行了比较。