Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.
"Tests for covariance matrix with fixed or divergent dimension." Ann. Statist. 41 (4) 2075 - 2096, August 2013. https://doi.org/10.1214/13-AOS1136