Covariance selection by thresholding the sample correlation matrix

This article shows that when the nonzero coefficients of the population correlation matrix are all greater in absolute value than (C1logp/n)1/2(C1logp/n)1/2 for some constant C1C1, we can obtain covariance selection consistency by thresholding the sample correlation matrix. Furthermore, the rate (logp/n)1/2(logp/n)1/2 is shown to be optimal.