The modified Cholesky decomposition (MCD) is an efficient technique for estimating a covariance matrix. However, it is known that the MCD technique often requires a pre-specified variable ordering in the estimation procedure. In this work, we propose a weighted average ensemble covariance estimation for high-dimensional data based on the MCD technique. It can flexibly accommodate the high-dimensional case and ensure the positive definiteness property of the resultant estimate. Our key idea is to obtain different weights for different candidate estimates by minimizing an appropriate risk function with respect to the Frobenius norm. Different from the existing ensemble estimation based on the MCD, the proposed method provides a sparse weighting scheme such that one can distinguish which variable orderings employed in the MCD are useful for the ensemble matrix estimate. The asymptotically theoretical convergence rate of the proposed ensemble estimate is established under regularity conditions. The merits of the proposed method are examined by the simulation studies and a portfolio allocation example of real stock data.

翻译：修正Cholesky分解（MCD）是一种估计协方差矩阵的有效技术。然而，众所周知，MCD技术在估计过程中通常需要预先指定变量顺序。在本研究中，我们提出了一种基于MCD技术的高维数据加权平均集成协方差估计方法。该方法能够灵活适应高维情况，并确保所得估计的正定性。我们的核心思想是通过最小化关于Frobenius范数的适当风险函数，为不同候选估计获得不同的权重。与现有基于MCD的集成估计不同，所提出的方法提供了一种稀疏加权方案，使得能够区分MCD中采用的哪些变量顺序对集成矩阵估计是有用的。在正则性条件下，建立了所提集成估计的渐近理论收敛速率。通过模拟研究和真实股票数据的投资组合配置实例，验证了所提方法的优点。