26 jan 2021 -- 15:30
G-meet
Abstract.
Maximum likelihood estimation is a method for estimating the parameters of a statistical model. In recent years, there has been much interest in tensor normal models, which are Gaussian statistical models where the covariance matrix has Kronecker product structure. In this talk, we discuss sample size thresholds for maximum likelihood estimation for tensor normal models: that is, we determine the minimal number of samples such that, almost surely, (1) the likelihood function is bounded from above, (2) maximum likelihood estimates (MLEs) exist, and (3) MLEs exist uniquely. We obtain a complete answer for both real and complex models as well as some interesting structural consequences. Along the way, we will see a recently discovered connection between maximum likelihood estimation and stability questions in geometric invariant theory, castling transforms, and results on stabilizers in general positions. This is joint work with Harm Derksen and Visu Makam.