We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish the Gumbel convergence of the maximum deviations. Our...

The constraint that a covariance matrix must be positive definite presents difficulties for modeling its structure. Pourahmadi (1999, 2000) [18,19] proposed a parameterization of the covariance matrix for univariate longitudinal data in which the parameters are unconstrained, which is based on...

Considering the covariance selection problem of multivariate normal distributions, we show that its Fenchel dual formulation is insightful and allows one to calculate direct estimates under decomposable models. We next generalize the covariance selection to multivariate dependence, which...