After reviewing a large body of literature on the modeling of bivariate discrete distributions with finite support, \cite{Gee20} made a compelling case for the use of the iterative proportional fitting procedure (IPFP), also known as Sinkhorn's algorithm or matrix scaling in the literature, as a sound way to attempt to decompose a bivariate probability mass function into its two univariate margins and a bivariate probability mass function with uniform margins playing the role of a discrete copula. After stating what could be regarded as a discrete analog of Skar's theorem, we investigate, for starting bivariate p.m.f.s with rectangular support, nonparametric and parametric estimation procedures as well as goodness-of-fit tests for the underlying discrete copula. Related asymptotic results are provided and build upon a new differentiability result for the iterative proportional fitting procedure which can be of independent interest. Theoretical results are complemented by finite-sample experiments and a data example.

翻译：在回顾了大量关于有限支撑二元离散分布建模的文献后，\cite{Gee20}有力地论证了使用迭代比例拟合过程（IPFP），文献中也称为Sinkhorn算法或矩阵缩放，作为将二元概率质量函数分解为两个单变量边缘分布和具有均匀边缘的二元概率质量函数（其作用类似于离散Copula）的合理方法。在陈述了可视为Sklar定理的离散类比之后，我们针对具有矩形支撑的初始二元概率质量函数，研究了非参数和参数估计方法以及底层离散Copula的拟合优度检验。相关渐近结果基于迭代比例拟合过程的一个新的可微性结果给出，该结果可能具有独立的研究价值。理论结果辅以有限样本实验和一个数据示例加以验证。