TWO SAMPLE TESTS FOR HIGH-DIMENSIONAL COVARIANCE MATRICES

• 成果类型: Article
• 署名作者: Li, Jun; Chen, Song Xi
• 署名单位: Iowa State University; Peking University; Peking University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS993
• 发表日期: 2012
• 页码: 908-940
• 关键词: largest eigenvalue; hypothesis tests; gene-expression; microarray; regularization; normalization; CATEGORIES; selection; sparsity; MODEL

摘要

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the large p, small n situations and (ii) without assuming parametric distributions for the two populations. These two aspects surpass the capability of the conventional likelihood ratio test. The proposed tests can be used to test on covariances associated with gene ontology terms.