A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor

Yuanyuan Jiang and Xingzhong Xu
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Yuanyuan Jiang: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Xingzhong Xu: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2022, vol. 10, issue 10, 1-23

Abstract: In classical statistics, the primary test statistic is the likelihood ratio. However, for high dimensional data, the likelihood ratio test is no longer effective and sometimes does not work altogether. By replacing the maximum likelihood with the integral of the likelihood, the Bayes factor is obtained. The posterior Bayes factor is the ratio of the integrals of the likelihood function with respect to the posterior. In this paper, we investigate the performance of the posterior Bayes factor in high dimensional hypothesis testing through the problem of testing the equality of two multivariate normal mean vectors. The asymptotic normality of the linear function of the logarithm of the posterior Bayes factor is established. Then we construct a test with an asymptotically nominal significance level. The asymptotic power of the test is also derived. Simulation results and an application example are presented, which show good performance of the test. Hence, taking the posterior Bayes factor as a statistic in high dimensional hypothesis testing is a reasonable methodology.

Keywords: high dimension; mean test; posterior Bayes factor; asymptotic normality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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