Differentiable evaluation of objective functions in sampling design with variance-covariance matrices

evaluation of fat atrophy in patients with dermis fat graft of orbit by ct-scan

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Eigenvalue variance bounds for covariance matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for Wigner matrices [7] and stated the results for covariance matrices. They are proved in the present paper. Relying on the LUE example, which needs to be investi...

Unconstrained parametrizations for variance-covariance matrices

The estimation of variance-covariance matrices in situations that involve the optimization of an objective function (e.g. a log-likelihood function) is usually a difficult numerical problem, since the resulting estimates should be positive semi-definite matrices. We can either use constrained optimization, or employ a parameterization that enforces this condition. We describe here five differen...

Covariance functions for mean square differentiable processes on spheres

Many applications in spatial statistics involve data observed over large regions on the Earth’s surface. There is a large statistical literature devoted to covariance functions capable of modeling the degree of smoothness in data on Euclidean spaces. We adapt some of this work to covariance functions for processes on spheres, where the natural distance is great circle distance. In doing so, we ...

Multivariate Analysis of Variance Using Patterned Covariance Matrices