论文标题
具有理性最大似然估计器的准独立模型
Quasi-independence models with rational maximum likelihood estimator
论文作者
论文摘要
我们对具有合理最大似然估计器或MLE的双向独立模型（或具有结构零的独立模型）进行分类。我们在与模型相关的两分图上提供了必要和充分的条件，以使MLE合理。在这种情况下，我们就此图的组合特征为MLE提供了一个明确的公式。我们还使用角统一来表明，对于一般日志线性模型，$ \ Mathcal {m} $带有理性MLE，这是通过限制到$ \ MATHCAL {M M} $的足够统计锥体所获得的任何模型，也有理性的MLE。
We classify the two-way independence quasi-independence models (or independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph associated to the model for the MLE to be rational. In this case, we give an explicit formula for the MLE in terms of combinatorial features of this graph. We also use the Horn uniformization to show that for general log-linear models $\mathcal{M}$ with rational MLE, any model obtained by restricting to a face of the cone of sufficient statistics of $\mathcal{M}$ also has rational MLE.
