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

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

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.

Suggested Citation

  • Wei Lan & Ronghua Luo & Chih-Ling Tsai & Hansheng Wang & Yunhong Yang, 2015. "Testing the Diagonality of a Large Covariance Matrix in a Regression Setting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 76-86, January.
    • Handle: RePEc:taf:jnlbes:v:33:y:2015:i:1:p:76-86
    DOI: 10.1080/07350015.2014.923317
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    Cited by:

    1. Xu, Kai & Hao, Xinxin, 2019. "A nonparametric test for block-diagonal covariance structure in high dimension and small samples," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 551-567.

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