论文标题
通过$ f $ divergence的特定表格的广义Cramér系数
Generalized Cramér's coefficient via $f$-divergence for contingency tables
论文作者
论文摘要
已经提出了双向应急表分析中的各种度量，以表达抗义表中的行变量和列变量之间的关联强度。 Tomizawa等。 （2004年）提出了更一般的措施，包括Cramér的系数，使用功率发散。在本文中，我们提出了使用$ f $ divergence的措施，该措施比电力差更宽。与统计假设检验不同，这些措施提供了应急表中关联结构的量化。我们的研究的贡献证明，应用满足$ f $ didivergence条件的函数的措施具有理想的特性，以衡量应急表中的关联性强度。通过这种贡献，我们可以使用具有分析师具有重要属性的差异来轻松构建一种新措施。例如，我们通过使用$θ$ - 差异的度量进行了数值实验。此外，我们可以进一步解释应急表中的行变量和列变量之间的关联，而这些变量无法用传统的变量获得。我们还显示了我们提出的措施与应急表中潜在变量的双变量正态分布中的相关系数之间的关系。
Various measures in two-way contingency table analysis have been proposed to express the strength of association between row and column variables in contingency tables. Tomizawa et al. (2004) proposed more general measures, including Cramér's coefficient, using the power-divergence. In this paper, we propose measures using the $f$-divergence that has a wider class than the power-divergence. Unlike statistical hypothesis tests, these measures provide quantification of the association structure in contingency tables. The contribution of our study is proving that a measure applying a function that satisfies the condition of the $f$-divergence has desirable properties for measuring the strength of association in contingency tables. With this contribution, we can easily construct a new measure using a divergence that has essential properties for the analyst. For example, we conducted numerical experiments with a measure applying the $θ$-divergence. Furthermore, we can give further interpretation of the association between the row and column variables in the contingency table, which could not be obtained with the conventional one. We also show a relationship between our proposed measures and the correlation coefficient in the bivariate normal distribution of latent variables in the contingency tables.
