ON THE EXISTENCE OF MAXIMUM-LIKELIHOOD ESTIMATORS FOR GRAPHICAL GAUSSIAN MODELS

In graphical Gaussian models, it is well known that the maximum likeli hood estimator exists with probability one if the number of replicates is at least as large as the number of variates. In this paper we deal with the case of fewer replicates. For the chordless p-cycle with two replicates, we prove that the maximum likelihood estimator exists wit h probability strictly between zero and one. (In case of p = 4 and ind ependence, the probability is 2/3.)