  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.
