Fuzzy empirical copula for estimating data dependence structure

Empirical copula is a non-parametric algorithm to estimate the dependence structure of high-dimensional arbitrarily distributed data. The computation of empirical copula is, however, very costly so that it cannot be implemented into applications at a real-time context. In this paper, fuzzy empirical copula is proposed to reduce the computation time of dependence structure estimation. First, a brief introduction of empirical copula is provided. Next, a new version of Fuzzy Clustering by Local Approximation of Memberships (FLAME) is proposed to integrate into empirical copula. The FLAME+ algorithm is utilised to identify the highest density objects, which are used to represent the original dataset, and then empirical copula is applied to estimate its dependence structure. Finally, two case studies have been carried out to demonstrate the effectiveness and efficiency of the fuzzy empirical copula.