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Covariance selection by thresholding the sample correlation matrix

Authors:	Binyan Jiang

Institution:	The Living Analytics Research Centre (LARC), Singapore Management University, Singapore; Carnegie Mellon University, Pittsburgh, PA 15213, United States

Abstract:	This article shows that when the nonzero coefficients of the population correlation matrix are all greater in absolute value than (_C₁logp/n)^1/2 ${(C_{1} log p / n)}^{1 / 2}$ for some constant _C₁ $C_{1}$ , we can obtain covariance selection consistency by thresholding the sample correlation matrix. Furthermore, the rate (logp/n)^1/2 ${(log p / n)}^{1 / 2}$ is shown to be optimal.

Keywords:	Bernstein type inequality Covariance selection Large correlation matrix Large covariance matrix Thresholding
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