Covariance matrix testing in high dimension using random projections

Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as traditional multivariate asymptotic theory no longer valid. When dimension larger than or increasing with sample size, standard likelihood based have poor performance. Existing dimensional are either computationally expensive very weak control of type I error. In this paper, we propose test procedure, CRAMP (covariance testing using random projections), hypotheses involving one more matrices projections. Projecting data randomly into lower subspaces alleviates curse dimensionality, allowing use tests. An extensive simulation study performed to compare against asymptotics-based procedures. application proposed method two gene expression sets presented.