论文标题
分层Aitchison-Silvey模型，用于不完整的二元样品空间
Hierarchical Aitchison-Silvey models for incomplete binary sample spaces
论文作者
论文摘要
当不可能的变量类别的某些组合时，多元样本空间可能是不完整的笛卡尔产品。传统的对数线性模型在这种情况下不适用于独立性和条件独立性，因为它们可能将正概率与不存在的细胞相关联。为了描述不完整的样本空间中的关联结构，本文开发了一类层次乘法模型，这些模型是通过设置某些非均匀的广义优势比来定义的，并以Aitchison和Silvey的名字命名，这些比率是最早考虑此类比率的人之一。这些模型是不包含整体效应的弯曲指数家族，从代数的角度来看，是非均匀的图火理想。该模型类别与对数线性模型和准对数线性模型的关系详细研究了统计和代数几何形状。还讨论了最大似然估计及其特性以及相关算法的存在。
Multivariate sample spaces may be incomplete Cartesian products, when certain combinations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do not apply in such cases, as they may associate positive probabilities with the non-existing cells. To describe the association structure in incomplete sample spaces, this paper develops a class of hierarchical multiplicative models which are defined by setting certain non-homogeneous generalized odds ratios equal to one and are named after Aitchison and Silvey who were among the first to consider such ratios. These models are curved exponential families that do not contain an overall effect and, from an algebraic perspective, are non-homogeneous toric ideals. The relationship of this model class with log-linear models and quasi log-linear models is studied in detail in terms of both statistics and algebraic geometry. The existence of maximum likelihood estimates and their properties, as well as the relevant algorithms are also discussed.
