Abstract
PurposeIn this paper, the authors applied the empirical likelihood method, which was originally proposed by Owen, to the copula moment based estimation methods to take advantage of its properties, effectiveness, flexibility and reliability of the nonparametric methods, which have limiting chi-square distributions and may be used to obtain tests or confidence intervals. The authors derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Design/methodology/approachIn this paper we applied the empirical likelihood method which originally proposed by Owen, to the copula moment based estimation methods.FindingsWe derive an asymptotically normal estimator of the empirical likelihood based on copula moment estimation methods (ELCM). Finally numerical performance with a simulation experiment of ELCM estimator is studied and compared to the CM estimator, with a good result.Originality/valueIn this paper we applied the empirical likelihood method which originally proposed by Owen 1988, to the copula moment based estimation methods given by Brahimi and Necir 2012. We derive an new estimator of copula parameters and the asymptotic normality of the empirical likelihood based on copula moment estimation methods.
Highlights
One of the main topics in multivariate statistical analysis is the statistical inference on the dependence parameter θ
Empirical likelihood for CM based estimation method We consider the Archimedean copula family defined by CðuÞ 1⁄4
We show that the empirical likelihood copula moment (ELCM) estimator is performs better than the CM based estimator in large one
Summary
One of the main topics in multivariate statistical analysis is the statistical inference on the dependence parameter θ. Many researchers investigated the copula parameter estimation, namely the methods of concordance [1, 2] fully and the pseudo maximum likelihood [3], inference function of margins [4, 5], minimum distance [6] and recently the copula moment and L-moment based estimation methods given in [7, 8]. Several authors investigated the empirical likelihood see for instance [12,13,14,15,16]. The advantage of this method is that the empirical likelihood has both effectiveness and flexibility of the likelihood method, and reliability of the non-parametric methods, and it helps. The authors are indebted to an anonymous referee for valuable remarks and suggestions
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