A note on asymptotics of classical likelihood ratio tests for high-dimensional normal distributions

Yuecai Han and Zhe Yin

Statistics & Probability Letters, 2023, vol. 199, issue C

Abstract: For random samples of size n obtained from m-variate normal distributions, we investigate the classical likelihood ratio tests for their means and covariance matrices in the high-dimensional case. Many researchers analyze the test statistics for the case of n going to infinity and m keeping fixed. In the high-dimensional setting, the objective of this paper is to prove that the likelihood ratio test statistics converge in distribution to normal distributions when both m and n go to infinity with m/n→y∈(0,1]. We obtain this conclusion very intuitively by using Lyapunov’s central limit theorem.

Keywords: Asymptotics; High-dimensional data; Likelihood ratio test; Lyapunov’s central limit theorem (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109859

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