On the phase transition of Wilks' phenomenon

• 成果类型: Article
• 署名作者: He, Yinqiu; Meng, Bo; Zeng, Zhenghao; Xu, Gongjun
• 署名单位: University of Michigan System; University of Michigan; Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa078
• 发表日期: 2021
• 页码: 741748
• 关键词: likelihood ratio tests; central limit-theorems; Empirical Likelihood; asymptotic-behavior; statistics; parameters; number

摘要

Wilks' theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the conventional Wilks' phenomenon of the likelihood ratio test statistic often fails. Although new approximations have been proposed in high-dimensional settings, there still lacks a clear statistical guideline regarding how to choose between the conventional and newly proposed approximations, especially for moderate-dimensional data. To address this issue, we develop the necessary and sufficient phase transition conditions for Wilks' phenomenon under popular tests on multivariate mean and covariance structures. Moreover, we provide an in-depth analysis of the accuracy of chi-squared approximations by deriving their asymptotic biases. These results may provide helpful insights into the use of chi-squared approximations in scientific practices.