Fast estimating data dependence structure via fuzzy empirical copula

As a non-parametric algorithm, empirical copula is an effective way to estimate the dependence structure of high-dimension arbitrarily distributed data. However, it suffers from the problem of huge computation time because of its high computational complexity. In this paper, fuzzy empirical copula is proposed to solve this problem by combining the fuzzy clustering by local approximation of memberships (FLAME) with empirical copula. In the proposed algorithm, FLAME is extended from two-dimension data to high-dimension data and FLAME⁺ is implemented to identify the highest density objects which represent the original dataset, and then empirical copula is used to estimate its independence structure according to the new dataset. Case studies have been carried out to demonstrate the effectiveness of the fuzzy empirical copula.