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

TL;DR

This paper introduces a new method for estimating dependence parameters in bivariate copula models using bivariate L-moments, demonstrating improved bias, efficiency, and robustness over traditional methods through extensive simulations.

Contribution

It establishes a novel link between bivariate L-moments and copula functions, providing a new, efficient estimation technique for multiparameter 2D copula models.

Findings

BLM-based estimation outperforms MLE, minimum distance, and rank Z-estimation in bias and computation time

The BLM method shows reasonable RMSE and robustness to outliers

Simulation results confirm the effectiveness of the proposed estimator for large samples

Abstract

Recently, Serfling and Xiao (2007) extended the L-moment theory (Hosking, 1990) to the multivariate setting. In the present paper, we focus on the two-dimension random vectors to establish a link between the bivariate L-moments (BLM) and the underlying bivariate copula functions. This connection provides 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 the BLM, the maximum likelihood, the minimum distance and rank approximate Z-estimation. The obtained results show that, when the sample size increases, BLM-based estimation performs better as far as the bias and computation time are concerned. Moreover, the root mean squared error (RMSE) is quite reasonable and less sensitive in general to outliers than those of the above cited methods. Further, we expect that the BLM method is an easy-to-use tool for the estimation of multiparameter copula models.