A well-conditioned estimator for large-dimensional covariance matrices
A well-conditioned estimator for large-dimensional covariance matrices
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DOI：
10.1016/s0047-259x(03)00096-4
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发表时间：
2004-02-01
影响因子：
1.6
通讯作者：
Wolf, M
中科院分区：
文献类型：
--
作者：
Ledoit, O;Wolf, M
许多应用问题要求协方差矩阵估计器不仅是可逆的，而且是良好条件的（即，求逆不会放大估计误差）。对于高维协方差矩阵，通常的估计量-样本协方差矩阵-通常不是条件良好的，甚至可能不是可逆的。本文介绍了一种估计，这是良好的条件和更准确的比样本协方差矩阵渐近。该估计量是无分布的，并且具有易于计算和解释的简单显式公式。它是样本协方差矩阵与单位矩阵的渐近最优凸线性组合。最优性是指相对于二次损失函数，随着观测值的数量和变量的数量一起趋于无穷大而渐近。广泛的Monte Carlo证实了渐近结果在有限样本下是成立的。(C)2003年爱思唯尔公司All rights reserved.
Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For large-dimensional covariance matrices, the usual estimator-the sample covariance matrix-is typically not well-conditioned and may not even be invertible. This paper introduces an estimator that is both well-conditioned and more accurate than the sample covariance matrix asymptotically. This estimator is distribution-free and has a simple explicit formula that is easy to compute and interpret. It is the asymptotically optimal convex linear combination of the sample covariance matrix with the identity matrix. Optimality is meant with respect to a quadratic loss function, asymptotically as the number of observations and the number of variables go to infinity together. Extensive Monte Carlo confirm that the asymptotic results tend to hold well in finite sample. (C) 2003 Elsevier Inc. All rights reserved.