论文标题
与特征值收缩的散射的m估计器
M-estimators of scatter with eigenvalue shrinkage
论文作者
论文摘要
一个受欢迎的正规化（收缩）协方差估计器是收缩样品协方差矩阵（SCM），该矩阵（SCM）具有与SCM相同的特征向量集，但缩小了其特征值的特征值。在本文中，考虑了一种更通用的方法，其中SCM被散点矩阵的M估计器和一种全自动数据自适应方法替换，以计算最佳的收缩参数，并提出了最小平均误差的最佳收缩参数。我们的方法允许使用任何重量功能，例如高斯，休伯或$ t $权重功能，所有这些功能都常用于M估计框架。我们的仿真示例表明，基于提出的最佳调整与强大的重量功能结合的收缩M估计器不会在数据为高斯时缩小性能以缩小SCM估计量，但是当从重型尾部分布中采样数据时，可以显着提高性能。
A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adaptive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Huber's, or $t$ weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from a heavy-tailed distribution.
