RMT “single-cluster” criterion for predicting large errors (outliers) in maximum-likelihood detection-estimation

We investigate the sudden onset of failure in maximum-likelihood (ML) detection-estimation on multivariate Gaussian models with a critically small number of data samples (observations). Using methods from random matrix theory (RMT) [also known as generalised statistical analysis (GSA) or G-analysis], we demonstrate that, for any set of true (exact) data parameters, we can identify a parametric space of covariance matrix models that are statistically as likely as the true one. The continuum of such equally likely models defines the nonidentifiability ldquoambiguity regionrdquo of the ML estimation (MLE). When this region includes models with completely erroneous parameters (ldquooutliersrdquo), MLE ldquoperformance breakdownrdquo is predicted.