Homogeneity test of several covariance matrices with high-dimensional data.

This article not only presents a test based on the well-known Box M test for testing the equality of several covariance matrices with high-dimensional data, but also gives the asymptotic distribution of the proposed test. Simulation and experimental studies illustrate that the proposed test performs well and can compete with other five known tests.

High-dimensional covariance matrices tests for analyzing multi-tumor gene expression data.

By collecting multiple sets per subject in microarray data, gene sets analysis requires characterize intra-subject variation using gene expression profiling. For each subject, the data can be written as a matrix with the different subsets of gene expressions (e.g. multiple tumor types) indexing the rows and the genes indexing the columns. To test the assumption of intra-subject (tumor) variation, we present and perform tests of multi-set sphericity and multi-set identity of covariance structures across subjects (tumor types). We demonstrate by both theoretical and empirical studies that the tests have good properties. We applied the proposed tests on The Cancer Genome Atlas (TCGA) and tested covariance structures for the gene expressions across several tumor types.