We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high dimensions. We prove convergence of the iterative part of our algorithm and demonstrate the favorable performance of the estimator in a wide range of simulation scenarios. Finally, an empirical application demonstrates its state-of-the-art performance on real data.

翻译：我们将Tyler稳健散度矩阵估计器与非线性压缩相结合。该方法为椭圆模型中的散度矩阵提供了一种简单且快速的估计器，既能应对重尾分布，也能处理高维数据。我们证明了算法迭代部分的收敛性，并在广泛的模拟场景中展示了该估计器的优越性能。最后，通过实证应用证明了其在真实数据上的先进性能。