Sampling multivariate count variables with prespecified Pearson correlation using marginal regular vine copulas. (English) Zbl 1474.62026

Yuan, Zhenfei; Hu, Taizhong

J. Univ. Sci. Technol. China 50, No. 10, 1291-1302 (2020).

Summary: The problem of sampling multivariate count variables has practical significance. Some previous researchers had proposed an algorithm for sampling multivariate count random variables based on C-vine copulas, by which the parameters \({\rho_{i, j|D}}\) of edge \({e_{i, j|D}}\) of the C-vine structure are estimated by optimizing the difference between the sample partial correlation \({\hat{\sigma}_{i, j|D}}\) and the partial correlation \({\sigma_{i, j|D}}\) 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 correlation \({\hat{\sigma}_{ij}}\) and the targeted correlation \({\sigma_{ij}}\) for pairs of variables. Three simulation studies illustrate that the new sampling method generates more accurate results than the C-vine sampling method and the Naive sampling method. The sampling algorithm routines are implemented in Python as package countvar in PyPi.

MSC:

62D05	Sampling theory, sample surveys
62H05	Characterization and structure theory for multivariate probability distributions; copulas

Keywords:

C-vine copula; marginal regular vine copula; multivariate count random variable; Naive sampling method

Software:

PyPI; countvar; Python