Testing the Diagonality of a Large Covariance Matrix in a Regression Setting

Wei Lan, Ronghua Luo, Chih-Ling Tsai, Hansheng Wang and Yunhong Yang

Journal of Business & Economic Statistics, 2015, vol. 33, issue 1, 76-86

Abstract: In multivariate analysis, the covariance matrix associated with a set of variables of interest (namely response variables) commonly contains valuable information about the dataset. When the dimension of response variables is considerably larger than the sample size, it is a nontrivial task to assess whether there are linear relationships between the variables. It is even more challenging to determine whether a set of explanatory variables can explain those relationships. To this end, we develop a bias-corrected test to examine the significance of the off-diagonal elements of the residual covariance matrix after adjusting for the contribution from explanatory variables. We show that the resulting test is asymptotically normal. Monte Carlo studies and a numerical example are presented to illustrate the performance of the proposed test.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:33:y:2015:i:1:p:76-86

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DOI: 10.1080/07350015.2014.923317

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