Asymptotic properties of scatter estimators for elliptical graphical models are studied. Such models impose a given pattern of zeros on the inverse of the shape matrix of an elliptically distributed random vector. In particular, we introduce the class of graphical M-estimators and compare them to plug-in M-estimators. It turns out that, under suitable conditions, both approaches yield the same asymptotic efficiency. Furthermore, the results of this paper apply to both decomposable and non-decomposable graphical models and so generalize the results for decomposable models given by Vogel & Fried (2011) for the plug-in M-estimators.
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