Projection tests for high-dimensional spiked covariance matrices

Testing the existence of low-dimensional perturbations or signals is very important, e.g., in factor analysis and signal processing. This paper aims to develop new tests for high-dimensional spiked covariance matrices based on a projection approach. The asymptotic distribution of the proposed tests is obtained under regularity conditions. We further explore a power enhancement technique under covariance matrix sparsity. The finite-sample enhanced power performance of the proposed tests is shown through simulations. A microarray dataset is used for illustration purposes.