基于边际正则藤copulas对具有既定皮尔逊相关系数的多元离散随机变量的抽样算法  

Sampling multivariate count variables with prespecified Pearson correlation using marginal regular vine copulas

作　　者：袁振飞[1] 胡太忠 Yuan Zhenfei;Hu Taizhong(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学管理学院统计金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2020年第10期1291-1302,共12页JUSTC

基　　金：This work was supported by the National Nature Science Foundation of China(Nos.71871208,11371340).

摘　　要：基于多元离散随机变量的抽样问题在实践中的应用价值,Erhardt和Czado提出了基于C藤Copulas的多元离散随机变量的抽样算法,其优化参数为C藤的边参数,目标函数为给定的皮尔逊偏相关系数与样本偏相关系数的距离.本文引入了边际正则藤Copulas的概念,进而直接以随机变量对的样本相关系数与给定的皮尔逊相关系数σij之间的距离为目标函数进行优化.三组模拟实验结果分别与文献[1]提出的基于C藤的抽样算法,文献[3]中使用的Naive基准抽样算法相比,基于边际正则藤Copula的抽样算法具有相对较高的精确性.本文中所使用的抽样算法通过Python语言实现并打包命名为countvar上传至PyPi.The problem of sampling multivariate count variables has practical significance.Ref.[1]proposed an algorithm for sampling multivariate count random variables based on C-vine copulas,by which the parametersρi,j|D of edge e i,j|D of the C-vine structure are estimated by optimizing the difference between the sample partial correlationσ︿i,j|D and the partial correlationσi,j|D calculated from the prespecified correlation matrix by the Pearson recurrence formula,where D is a conditioning node set.We introduce the concept of marginal regular vine copula,which leads to directly optimizing the difference between the sample correlationσ︿ij and the targeted correlationσij for pairs of variables.Three simulation studies illustrate that the new sampling method generates more accurate results than the C-vine sampling method in Ref.[1]and the Naive sampling method in Ref.[3].The sampling algorithm routines are implemented in Python as package countvar in PyPi.

关 键 词：C藤Copula 边际正则藤Copula 多远离散随机变量 Naive抽样算法 正则藤 抽样 

分 类 号：O212.2[理学—概率论与数理统计]