A multiple testing approach to the regularisation of large sample correlation matrices
A multiple testing approach to the regularisation of large sample correlation matrices
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DOI：
10.1016/j.jeconom.2018.10.006
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发表时间：
2019-02-01
影响因子：
6.3
通讯作者：
Smith, L. Vanessa
中科院分区：
文献类型：
--
作者：
Bailey, Natalia;Pesaran, M. Hashem;Smith, L. Vanessa
本文提出了一种利用多重检验(MT)文献中的见解来估计大协方差矩阵的正则化方法。该方法测试单个成对相关性的统计意义，并考虑到问题的多重测试性质，将那些在统计上不显著的元素设置为零。试验的有效p值被设置为N(横截面维度)的递减函数，其速率由基础观测的相关性的性质以及N和T(时间维度)的相对扩展速率控制。在这方面，该方法指定要在高斯和非高斯设置下使用的适当阈值参数。只要真协方差矩阵是稀疏的，则样本相关矩阵的MT估计在谱和Frobenius范数下是一致的，在支持恢复方面是一致的。使用蒙特卡罗实验将所提出的MT估计器的性能与文献中的其他一些估计器进行了比较。结果表明，MT估计器表现良好，并且往往优于其他估计器，特别是当N大于T(C)2018 Elsevier B.V.时。保留所有权利。
This paper proposes a regularisation method for the estimation of large covariance matrices that uses insights from the multiple testing (MT) literature. The approach tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not statistically significant, taking account of the multiple testing nature of the problem. The effective p-values of the tests are set as a decreasing function of N (the cross section dimension), the rate of which is governed by the nature of dependence of the underlying observations, and the relative expansion rates of N and T (the time dimension). In this respect, the method specifies the appropriate thresholding parameter to be used under Gaussian and non-Gaussian settings. The MT estimator of the sample correlation matrix is shown to be consistent in the spectral and Frobenius norms, and in terms of support recovery, so long as the true covariance matrix is sparse. The performance of the proposed MT estimator is compared to a number of other estimators in the literature using Monte Carlo experiments. It is shown that the MT estimator performs well and tends to outperform the other estimators, particularly when N is larger than T. (C) 2018 Elsevier B.V. All rights reserved.