For minimization, the inversion of the matrices in these formulas is done so that negative eigenvalues are considered zero, resulting always in a positive semidefinite covariance matrix. In small ...

The formula is motivated by some recent and some old developments in random matrix theory and a requirement that it be explicitly invariant under a change of basis of risk factors. It may naturally be ...

Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for testing the equality of a covariance matrix, equality of a mean vector and a covariance matrix, independence ...

A new formula for converting a covariance matrix estimated in local currencies into a covariance matrix expressed in a common currency is proposed. This process uses simple matrix multiplications. We ...

This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of ...

The estimated covariance matrix of the parameter estimates is computed as the inverse Hessian matrix, and for unconstrained problems it should be positive definite. If the final parameter estimates ...