Robust concentration graph model selection

Concentration graph models are an attractive tool to explore the conditional independence structure in a multivariate normal distribution. In applications, in absence of a priori knowledge, it is possible to select the graph underlying a set of data through an appropriate model selection procedure. The recently proposed procedure, SINful, is appealing but sensitive to outliers, as it utilizes the sample estimator of the covariance matrix. A method to make the SINful procedure robust with respect to the presence of outlying observations, is proposed. This is based on the minimum covariance determinant (MCD) estimator for the variance-covariance matrix. A simulation study shows the advantages of this method.