Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	许王莉教授,中国人民大学
Inviter:
Title:	Fixed Effects Bayesian Testing in High-Dimensional Linear Mixed Models
Language:	Chinese
Time & Venue:	2022.12.05 10:30-12:00 腾讯会议: 127327155
Abstract:	Hypothesis testing on high-dimensional fixed effects is indispensable for investigating the utility of the predictors on response. In this case, the conventional frequentist methods designed for cases with fixed dimension fail completely since the dimension is larger than the sample size. Based on Bayes factor, a novel statistic is proposed for testing high-dimensional fixed effects. By transferring the linear mixed model, we build a bridge between the Bayes factor and the mimic likelihood ratio statistic of the modified model and provide a convictive justification for testing high-dimensional fixed effects through the mimic likelihood ratio statistic. The proposed statistic can be represented as the ratio of two quadratic forms constructed based on the random effects and random noises. In contrast to the existing results for quadratic forms based on independent and identically distributed random variable sequence, we investigate the asymptotic normality for the quadratic form constructed by independent but not identically distributed random sequence. This theoretical result itself is very rewarding. To put the test procedure into practice, a one-step iteration method is innovatively developed to determine the critical value. The power function under local alternative is derived with some mild conditions. In numerical experiments, we demonstrate the higher powers in comparison with the existing method and the practical utility of the proposed method