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Moderate deviation principle for likelihood ratio test in multivariate linear regression model

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  • Bai, Yansong
  • Zhang, Yong
  • Liu, Congmin

Abstract

Consider a multivariate linear regression model where the sample size is n and the dimensions of the predictors and the responses are p and m, respectively. We know that the limiting distribution of the likelihood ratio test (LRT) in multivariate linear regressions is different in the case of finite and high dimensions. In traditional multivariate analysis, when the dimension parameters (p,m) are fixed, the limiting distribution of the LRT is a χ2 distribution. However, in the high-dimensional setting, the χ2 approximation to the LRT may be invalid. In this paper, based on He et al. (2021), we give the moderate deviation principle (MDP) results for the LRT in a high dimensional setting, where the dimension parameters (p,m) are allowed to increase with the sample size n. The performance of the numerical simulation confirms our results.

Suggested Citation

  • Bai, Yansong & Zhang, Yong & Liu, Congmin, 2023. "Moderate deviation principle for likelihood ratio test in multivariate linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:jmvana:v:194:y:2023:i:c:s0047259x22001300
    DOI: 10.1016/j.jmva.2022.105139
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    References listed on IDEAS

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    8. Jiang Hu & Zhidong Bai & Chen Wang & Wei Wang, 2017. "On testing the equality of high dimensional mean vectors with unequal covariance matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 365-387, April.
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