High-Dimensional Two-Sample Covariance Matrix Testing via Super-Diagonals

He, Jing; Chen, Song Xi

doi:10.5705/ss.202017.0213

Cited by 4 publications

(1 citation statement)

References 33 publications

(27 reference statements)

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“…These tests can be categorized as L 2 -type tests. A two-sample covariance test based on super-diagonals was proposed by He and Chen (2018) whose test turned out to be more powerful than other existing tests when Σ 1 and Σ 2 have bandable structures. However, the aforementioned tests target dense signals, where most of components of Σ 1 −Σ 2 are nonzero.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Optimal Two-sample Tests in High-dimension

Lee¹,

You²,

Lin³

2021

Preprint

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We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that only a few entries of two mean vectors or covariance matrices are different. Many existing tests that rely on aggregating the difference between empirical means or covariance matrices are not optimal or yield low power under such setups. Motivated by this, we develop Bayesian two-sample tests employing a divide-andconquer idea, which is powerful especially when the difference between two populations is sparse but large. The proposed two-sample tests manifest closed forms of Bayes factors and allow scalable computations even in high-dimensions. We prove that the proposed tests are consistent under relatively mild conditions compared to existing tests in the literature. Furthermore, the testable regions from the proposed tests turn out to be optimal in terms of rates. Simulation studies show clear advantages of the proposed tests over other state-of-the-art methods in various scenarios. Our tests are also applied to the analysis of the gene expression data of two cancer data sets.

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Section: Introductionmentioning

confidence: 99%