Empirical likelihood test for the equality of several high-dimensional covariance matrices

The testing covariance equality is of importance in many areas of statistical analysis, such as microarray analysis and quality control. Conventional tests for the finite-dimensional covariance do not apply to high-dimensional data in general, and tests for the high-dimensional covariance in the literature usually depend on some special structure of the matrix and whether the dimension diverges. In this paper, we propose a jack-knife empirical likelihood method to test the equality of covariance matrices. The asymptotic distribution of the new test is regardless of the divergent or fixed dimension. Simulation studies show that the new test has a very stable size with respect to the dimension and it is also more powerful than the test proposed by Schott (2007) and studied by Srivastava and Yanagihara (2010). Furthermore, we illustrate the method using a breast cancer dataset.