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1 results

  • Maximum likelihood estimation for tensor normal models via castling transforms

  • Part of
  • Harm Derksen, Visu Makam, Michael Walter
  • Journal:
    Forum of Mathematics, Sigma / Volume 10 / 2022
    Published online by Cambridge University Press:
    01 July 2022, e50
    • Article
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  • 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.