On generalizing Gaussian graphical models

We explore elliptical graphical models as a generalization of Gaussian graphical models, that is, we allow the population distribution to be elliptical instead of normal. Towards a statis-tical theory for such graphical models, consisting of estimation, testing and model selection, we consider the problem of estimating partial correlations. We derive the asymptotic distri-bution of a class of partial correlation matrix estimators based on affine equivariant scatter estimators