Sphericity Test Of Covariance Matrix

As a basic statistical inference,hypothesis testing or significance test is an important branch of mathematical statistics.Testing for covariance matrix is one of important parametric hypothesis testing problems under multivariate normal population.With the rapid development of technology the data dimension increases greatly in the big data,and the classic test are no longer available.The classic test fails when the number of dimensions is greater than the sample size.In this paper we propose a test for sphericity of covariance matrix.The test statistic is constructed through the posterior Bayes factors.It is proved that the asymptotic null distribution is the chi-square distribution when the dimension is fixed.The test statistic is further corrected for dimension varying bellow n-1.The simulations show that the new statistic follows the standard normal distribution.