  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.
