Tests for High-Dimensional Covariance Matrices

By Songxi Chen, Lixu Zhang, Pingshou Zhong. Random Matrices. Theory and Applications, 2010

244 citations recorded by the source corpus.

We propose tests for sphericity and identity of high-dimensional covariance matrices. The tests are nonparametric without assuming a specific parametric distribution for the data. They can accommodate situations where the data dimension is much larger than the sample size, namely the “large p, small n” situations. We demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes. We applied the proposed test on a microarray dataset on Yorkshire Gilts and tested for the covariance structure for the expression levels for sets of genes.

Subfields: Genetics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/aba8c29309d9dc756b437dfc17b9693097a00711

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Tommaso Cai
2. Michael Wolf
3. Olivier Ledoit

In Molecular Biology

1. Zhaojun Wang
2. Tommaso Cai
3. Bu Zhou
4. Jia Guo
5. Michael Wolf
6. Ming-Yen Cheng
7. Changliang Zou
8. Olivier Ledoit

Citations in the corpus

• Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem (2016, background): “…Bai and Saranadasa (1996), Srivastava andDu (2008), andChen andQin (2010) for two-sample tests for means, Ledoit and Wolf (2002), Schott (2005), Chen, Zhang, and Zhong (2010), and Zou et al. (2014) for testing a specific covariance structure, Goeman, Van CONTACT Zhaojun Wang…”
• A Simple Two-Sample Test in High Dimensions Based on L2-Norm (2020, background): “…the ideas of the proposed test can be extended to other high-dimensional testing problems, including testing equality of means under unequal covariance matrices, testing equality of covariance matrices (Chen, Zhang, and Zhong 2010; Zhang, Peng, and Wang 2013), testing regression means, and so on.”
• Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, methodology): “A U -statistics based test that is similar to the one proposed in Chen et al. (2010) is shown to be rate optimal over this asymptotic regime.”
• Quadratic Shrinkage for Large Covariance Matrices (2020, background): “, 2013), and neuroscience (Deligianni et al., 2014), to highlight but a selected few. This literature also incorporates numerous extensions, adaptations and refinements of Ledoit and Wolf’s linear shrinkage estimator. For example, Schäfer and Strimmer (2005) propose six different shrinkage targets. ”