论文标题
矩阵正常模型的最大似然估计。
Maximum likelihood estimation for matrix normal models via quiver representations
论文作者
论文摘要
在本文中，我们研究了真实模型和复杂模型的矩阵正常模型的对数似然函数和最大似然估计（MLE）。我们描述了（几乎可以肯定）三个条件所需的确切样本数量，即界数可能的函数，MLE的存在和MLE的独特性。结果，我们观察到，几乎确定的对数样函数的界限几乎可以确保MLE的存在，从而证明了Drton，Kuriki和Hoff的猜想。我们使用的主要工具是从箭量表示理论中，特别是KAC，KING和Schofield在规范分解和稳定性方面的结果。
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three conditions, namely a bounded log-likelihood function, existence of MLEs, and uniqueness of MLEs. As a consequence, we observe that almost sure boundedness of log-likelihood function guarantees almost sure existence of an MLE, thereby proving a conjecture of Drton, Kuriki and Hoff. The main tools we use are from the theory of quiver representations, in particular, results of Kac, King and Schofield on canonical decomposition and stability.
