Invariant Theory and Matrix Normal Models

We describe connections between invariant theory and maximum likelihood estimation (ML estimation), in the context of matrix normal models. Namely, we link ML estimation in that case to the left right action of SLxSL on tuples of matrices. This enables us to characterize ML estimation by stability under that group action. Furthermore, invariant theory provides a new upper bound on the sample size for generic boundedness of the log-likelihood function. To illuminate the theory the talk puts emphasis on several examples. At the end we briefly outline how our results generalize to Gaussian group models.

Based on joint work with Carlos Améndola, Kathlén Kohn and Anna Seigal. This is the second part of a two part talk: in the first part, Anna Seigal will discuss our results for log-linear models.