A Powerful Bayesian Test for Equality of Means in High Dimensions

• 成果类型: Article
• 署名作者: Zoh, Roger S.; Sarkar, Abhra; Carroll, Raymond J.; Mallick, Bani K.
• 署名单位: Texas A&M University System; Texas A&M University College Station; Duke University; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1371024
• 发表日期: 2018
• 页码: 1733-1741
• 关键词: 2-sample test

摘要

We develop a Bayes factor-based testing procedure for comparing two population means in high-dimensional settings. In large-p-small-n settings, Bayes factors based on proper priors require eliciting a large and complex p x p covariance matrix, whereas Bayes factors based on Jeffrey's prior suffer the same impediment as the classical Hotelling T-2 test statistic as they involve inversion of ill-formed sample covariance matrices. To circumvent this limitation, we propose that the Bayes factor be based on lower dimensional random projections of the high-dimensional data vectors. We choose the prior under the alternative to maximize the power of the test for a fixed threshold level, yielding a restricted most powerful Bayesian test (RMPBT). The final test statistic is based on the ensemble of Bayes factors corresponding to multiple replications of randomly projected data. We show that the test is unbiased and, under mild conditions, is also locally consistent. We demonstrate the efficacy of the approach through simulated and real data examples. Supplementary materials for this article are available online.