论文标题
通过COPULAS建模计数数据
Modeling Count Data via Copulas
论文作者
论文摘要
Copula模型已被广泛用于建模连续随机变量之间的依赖性，但是通过Copulas进行建模计数数据最近在统计文献中变得流行。 Spearman的Rho是测量两个随机变量之间依赖性程度的合适工具。在本文中，当两个随机变量离散时，我们通过Copulas得出了Spearman的Rho相关性的总体版本。对于某些简单结构（例如具有不同边缘分布）的简单结构（例如Archimedean Copulas），获得了Spearman相关性的闭合形式表达式。我们为Bernoulli随机变量得出了Spearman Rho的上限和下限。然后，将拟议的Spearman的Rho相关性与其相应的Kendall的Tau值进行了比较。在某些特殊情况下，我们表征了这两种依赖度量之间的功能关系。进行了广泛的仿真研究，以证明我们的理论结果的有效性。最后，我们提出了一个双变量copula回归模型，以分析\ emph {宫颈癌}数据集的计数数据。
Copula models have been widely used to model the dependence between continuous random variables, but modeling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective tool to measure the degree of dependence between two random variables. In this paper, we derived the population version of Spearman's rho correlation via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas of simple structure such as Archimedean copulas with different marginal distributions. We derive the upper bound and the lower bound of the Spearman's rho for Bernoulli random variables. Then, the proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values. We characterize the functional relationship between these two measures of dependence in some special cases. An extensive simulation study is conducted to demonstrate the validity of our theoretical results. Finally, we propose a bivariate copula regression model to analyze the count data of a \emph{cervical cancer} dataset.
