Power Research Of Testing Equality Of Two Population Covariance Matrices

The rapid development and wide application of computer techniques permits tocollect and store a huge amount data, where the number of measured variables isusually large．Such high-dimensional data occur in many modern scientific fields,such as micro-array data in biology, making digitalization of space probes, stockmarket analysis in finance and wireless communication networks．However, it isfound that when dealing with large dimensional data, many classical statisticalprocedures induce large, even intolerable errors．Bai and Silverstein (2004) had proved the central limit theorems (CLT) for linearspectral statistics of large dimensional sample covariance matrices．Zheng(2012) hadproved CLT for linear spectral statistics (LSS) of F matrix．Zheng(2013) had provedCLT for linear spectral statistics (LSS) of the general F-matrix．Therefore, this paperdiscussed the power of testing equality of two population covariance matrices．The power of hypothesis testing is an important index to measure the quality ofa test method．The power is the probability of rejecting the null hypothesis when thealternative hypothesis is true．In this paper，we obtain the Stieltjes transform of F matrices limiting spectraldistribution by means of the binary non-linear equations，and make use of thetheoretical results of Zheng(2013) to solve mean and variance． At last, we obtain thepower value of testing equality of two population covariance matrices．...