论文标题
通过castling变换，张量正常模型的最大似然估计
Maximum likelihood estimation for tensor normal models via castling transforms
论文作者
论文摘要
在本文中，我们研究了样本量阈值，以张张量正常模型的最大似然估计。鉴于模型参数和样品的数量，我们确定几乎可以肯定的是（1）可能函数从上方界定，（2）最大似然估计（MLE），并且（3）MLE独特存在。我们为真实和复杂的模型获得了完整的答案。结果的结果是，几乎确定的对数样函数的界限几乎可以确保MLE的存在几乎确定。我们的技术基于不变理论和铸造变换。
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.
