Bivariate L-moments: A Hybrid Estimation Approach for Dependence and Marginal Parameters with Applications to Bivariate Pareto Models

Abstract

Multivariate extensions of L-moments — robust linear functions of order statistics — remain relatively underexplored despite their success in the univariate case. In this paper, we discuss a hybrid methodology for bivariate parameter estimation by combining bivariate L-moments with univariate L-moment techniques. We develop nonparametric estimators for bivariate L-comoment coefficients and propose a sequential three-step estimation procedure specifically designed to overcome the limitations of the Inference Function for Margins (IFM) method when parameters are shared across marginal and joint distributions. We illustrate our method with bivariate Pareto distributions, which are commonly used in modeling heavy-tailed phenomena. Simulation studies show that the proposed estimator performs better in terms of bias and root mean squared error (RMSE).