Upper and lower bounds for the eigenvalues of three types of matrices M are established. If M is written as the sum of a diagonal matrix D plus a matrix A, the real parts of the eigenvalues of M must ...

We test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be much larger or smaller than the nonspiked ones. For high-dimensional problems, we first ...

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 ...