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

Yansong Bai, Yong Zhang and Congmin Liu

Journal of Multivariate Analysis, 2023, vol. 194, issue C

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.

Keywords: High-dimensional data; Likelihood ratio test; Moderate deviation principle; Multivariate linear regression; Regression coefficient matrix (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2022.105139

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