Power computation for hypothesis testing with high-dimensional covariance matrices

Abstract

Based on the random matrix theory, a unified numerical approach is developed for power calculation in the general framework of hypothesis testing with high-dimensional covariance matrices. In the central limit theorem of linear spectral statistics for sample covariance matrices, the theoretical mean and covariance are computed numerically. Based on these numerical values, the power of the hypothesis test can be evaluated, and furthermore the confidence interval for the unknown parameters in the high-dimensional covariance matrix can be constructed. The validity of the proposed algorithms is well supported by a convergence theorem. Our numerical method is assessed by extensive simulation studies, and a real data example of the S&P 100 index data is analyzed to illustrate the proposed algorithms.