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Recently, Serfling and Xiao (2007) extended the L-moment theory (Hosking,1990) to the multivariate setting. In the present paper, we focus on thetwo-dimension random vectors to establish a link between the bivariateL-moments (BLM) and the underlying bivariate copula functions. This connectionprovides a new estimate of dependence parameters of bivariate statistical data.Consistency and asymptotic normality of the proposed estimator are established.Extensive simulation study is carried out to compare estimators based on theBLM, the maximum likelihood, the minimum distance and rank approximateZ-estimation. The obtained results show that, when the sample size increases,BLM-based estimation performs better as far as the bias and computation timeare concerned. Moreover, the root mean squared error (RMSE) is quite reasonableand less sensitive in general to outliers than those of the above citedmethods. Further, we expect that the BLM method is an easy-to-use tool for theestimation of multiparameter copula models.

Copula representation of bivariate L-moments : A new estimation method for multiparameter 2-dimentional copula models