This paper proposes a novel regularisation method for the estimation of large covariance matrices, which makes use of insights from the multiple testing literature. The method tests the statistical significance of individual pair-wise correlations and sets to zero those elements that are not...

This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X Nd. This test is applicable if the sample size, n + 1, and d both go to infinity while d/n ! y 2 (0,1), provided that the limits of tr(k)/d, k = 1, . . . , 8, are finite. The main...