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An improved banded estimation for large covariance matrix
Communications in Statistics - Theory and Methods ( IF 0.8 ) Pub Date : 2021-04-05 , DOI: 10.1080/03610926.2021.1910839
Wenyu Yang 1 , Xiaoning Kang 2
Affiliation  

Abstract

The modified Cholesky decomposition (MCD) is a powerful and efficient tool for the large covariance matrix estimation, which guarantees the positive definite property of the estimated matrix. However, when implementing the MCD, it requires a pre-knowledge of the variable ordering, which is often unknown before analysis or does not exist for some real data. In this work, we propose a positive definite Cholesky-based estimate for the large banded covariance matrix by recovering the variable ordering before applying the MCD technique. The asymptotically theoretical convergence rate is established under some regularity conditions. The merits of the proposed model is illustrated by simulation study and applications to two gene expression data sets.



中文翻译:

大协方差矩阵的改进带状估计

摘要

改进的Cholesky分解(MCD)是大协方差矩阵估计的强大而有效的工具,它保证了估计矩阵的正定性。然而,在实现 MCD 时,需要预先了解变量排序,这在分析之前通常是未知的,或者对于某些真实数据不存在。在这项工作中,我们通过在应用 MCD 技术之前恢复变量排序,为大带状协方差矩阵提出了基于 Cholesky 的正定估计。渐近理论收敛速度是在一定的规律性条件下建立的。通过模拟研究和对两个基因表达数据集的应用说明了所提出模型的优点。

更新日期:2021-04-05
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