Jackknife empirical likelihood for parametric copulas

Abstract

For fitting a parametric copula to multivariate data, a popular way is to employ the so-called pseudo maximum likelihood estimation proposed by Genest, Ghoudi, and Rivest. Although interval estimation can be obtained via estimating the asymptotic covariance of the pseudo maximum likelihood estimation, we propose a jackknife empirical likelihood method to construct confidence regions for the parameters without estimating any additional quantities such as the asymptotic covariance. A simulation study shows the advantages of the new method in case of strong dependence or having more than one parameter involved.

Keywords:

• copulas
• empirical likelihood
• interval estimation
• jackknife

Acknowledgements

We thank a reviewer for helpful comments. Peng's research was supported by NSA Grant H98230-10-1-0170 and NSF Grant DMS-1005336. Yang's research was partly supported by the National Basic Research Program (973 Program) of China (2007CB814905) and the National Natural Science Foundation of China (Grants No. 11131002).