A test for the identity of a high-dimensional correlation matrix based on the?4-norm

摘要

This paper presents a new test procedure for the identity of a correlation matrix in high-dimensional asymptotic frameworks, the statistic of which is based on the l4-norm of off-diagonal entries of the covariance matrix. A striking finding is that this test can achieve full power against both dense alternatives and sparse ones. Simulation results demonstrate its superiority over some competitors in various cases.

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