Large covariance or correlation matrix is frequently assumed to be sparse in that a number of the off-diagonal elements of the matrix are zero. This paper focuses on estimating the sparsity of a large population covariance matrix using a sample correlation matrix under multivariate normal...

This article shows that when the nonzero coefficients of the population correlation matrix are all greater in absolute value than (C1logp/n)1/2 for some constant C1, we can obtain covariance selection consistency by thresholding the sample correlation matrix. Furthermore, the rate (logp/n)1/2 is...