LAUSR

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 realtime context. In this chapter, 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 be integrated into empirical copula. The FLAME\(^+\) algorithm is implemented to identify the highest density objects which are used to represent the original dataset and then empirical copula is used to estimate its independence structure. Finally, two case studies have been carried out to demonstrate the effectiveness and efficiency of the fuzzy empirical copula.