Maximum likelihood estimation for matrix normal models via quiver representations
Abstract
In this paper, we study the loglikelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three conditions, namely a bounded loglikelihood function, existence of MLEs, and uniqueness of MLEs. As a consequence, we observe that almost sure boundedness of loglikelihood function guarantees almost sure existence of an MLE, thereby proving a conjecture of Drton, Kuriki and Hoff. The main tools we use are from the theory of quiver representations, in particular, results of Kac, King and Schofield on canonical decomposition and stability.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.10206
 Bibcode:
 2020arXiv200710206D
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Statistics Theory;
 13A50;
 14L24;
 14P05;
 16G20;
 20G45;
 62F10;
 62R01
 EPrint:
 26 pages