Please use this identifier to cite or link to this item: https://doi.org/10.1214/09-AOS694
Title: Corrections to LRT on large-dimensional covariance matrix by RMT
Authors: Bai, Z. 
Jiang, D.
Yao, J.-F.
Zheng, S.
Keywords: High-dimensional data
Marčenko-pastur distributions
Random F-matrices
Testing on covariance matrices
Issue Date: Dec-2009
Citation: Bai, Z., Jiang, D., Yao, J.-F., Zheng, S. (2009-12). Corrections to LRT on large-dimensional covariance matrix by RMT. Annals of Statistics 37 (6 B) : 3822-3840. ScholarBank@NUS Repository. https://doi.org/10.1214/09-AOS694
Abstract: In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension p is large compared to the sample size n. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tests to cope with high-dimensional effects. The asymptotic distributions of these corrected tests under the null are given. Simulations demonstrate that the corrected LR tests yield a realized size close to nominal level for both moderate p (around 20) and high dimension, while the traditional LR tests with χ 2 approximation fails. Another contribution from the paper is that for testing the equality between two covariance matrices, the proposed correction applies equally for non-Gaussian populations yielding a valid pseudo-likelihood ratio test. © Institute of Mathematical Statistics, 2009.
Source Title: Annals of Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/105074
ISSN: 00905364
DOI: 10.1214/09-AOS694
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