Robust estimators for non-decomposable elliptical graphical models

TL;DR

This paper investigates the asymptotic behavior of scatter estimators in elliptical graphical models, introducing graphical M-estimators and comparing their efficiency to plug-in estimators, applicable to both decomposable and non-decomposable models.

Contribution

It introduces the class of graphical M-estimators and demonstrates their asymptotic efficiency, extending previous results to non-decomposable models.

Findings

Graphical M-estimators have the same asymptotic efficiency as plug-in estimators under certain conditions.

Results apply to both decomposable and non-decomposable elliptical graphical models.

The study generalizes earlier findings for decomposable models to a broader class.

Abstract

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.