Plug-in Estimation of Dependence Characteristics of Archimedean Copula via Bézier Curve

Abstract

This article introduces measurement of the dependence between variables with a dependence structure defined by Archimedean copulas. The estimation of the dependence measure, such as Kendall’s tau as well as the lower and upper tail dependence, is investigated by using estimation of the Kendall distribution function based on the Bézier curve. A Monte Carlo study is performed to measure the performance of the new estimation method. The simulation results showed that the proposed methods has good results in terms of estimation performance. The new estimators are also used to estimate the dependence coefficients for three sets of real data.