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.
翻译：Copula 模型被广泛用来模拟连续随机变量之间的依赖性,但最近通过 Copulas 模拟计数数据在统计文献中变得很受欢迎。 Spearman 的 rho 是衡量两个随机变量之间依赖性的适当而有效的工具。 在本文中, 当两个随机变量都互不关联时, 我们通过 copula 得出Spearman 的 rho 相关性的人口版 。 Spearman 的 rho 值。 Spearman 的 commo 相关性的封闭式表达方式是针对一些简单结构的相册的, 比如Archimede coulas 具有不同边际分布的 。 我们从 Spearman 的 rho 的 rho 值的上方和下方框中得出 Bernoulli 随机变量的值。 然后, 拟议的 Spearman rho 的 相关性将与其对应的 Kendall tau 值进行比较。 我们在一些特殊情况下对这两种依赖性衡量标准之间的功能关系进行了描述。 进行了广泛的模拟研究, 以证明我们理论结果的有效性。 最后, 我们提出一个bivilvate colula 来分析一个计算结果的数据的计算模型。
相关内容
微信扫码咨询专知VIP会员