# Copula Density Estimation by Finite Mixture of Parametric Copula Densities

## TL;DR

This paper introduces a novel copula density estimation method using a finite mixture of various parametric copulas, effectively modeling complex dependencies in high-dimensional data.

## Contribution

It proposes a new mixture model combining multiple parametric copulas and compares an interior-point algorithm with EM for parameter estimation.

## Key findings

- Effective in modeling complex dependencies in high-dimensional data
- Interior-point algorithm outperforms EM in parameter estimation
- Demonstrated success on simulation and real datasets

## Abstract

A Copula density estimation method that is based on a finite mixture of heterogeneous parametric copula densities is proposed here. More specifically, the mixture components are Clayton, Frank, Gumbel, T, and normal copula densities, which are capable of capturing lower tail,strong central, upper tail, heavy tail, and symmetrical elliptical dependence, respectively. The model parameters are estimated by an interior-point algorithm for the constrained maximum likelihood problem. The interior-point algorithm is compared with the commonly used EM algorithm. Simulation and real data application show that the proposed approach is effective to model complex dependencies for data in dimensions beyond two or three.