Maximum Likelihood Estimation for Matrix Normal Models via Quiver Representations

We study the log-likelihood function and maximum likelihood estimate (MLE) for matrix normal model both real complex models. describe exact number of samples needed to achieve (almost surely) three conditions, namely a bounded function, existence MLEs, uniqueness MLEs. As consequence, we observe that almost sure boundedness guarantees an MLE, thereby proving conjecture Drton, Kuriki, Hoff [Existence Uniqueness Kronecker Covariance preprint, arXiv:2003.06024, 2020]. The main tools use are from theory quiver representations, in particular, results Kac, King, Schofield on canonical decomposition stability.