Maximum likelihood estimation for tensor normal models via castling transforms
Harm Derksen, Visu Makam, Michael Walter
Abstract
Abstract In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, 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. One consequence of our results is that almost sure boundedness of the log-likelihood function guarantees almost sure existence of an MLE. Our techniques are based on invariant theory and castling transforms.
Topics & Concepts
Maximum likelihoodMathematicsMaximum likelihood sequence estimationEstimationTensor (intrinsic definition)Applied mathematicsStatisticsPure mathematicsEconomicsManagementMarkov Chains and Monte Carlo MethodsTensor decomposition and applicationsStatistical Methods and Inference