EM algorithms for estimating the Bernstein copula

TL;DR

This paper introduces EM algorithms for estimating Bernstein copulas, demonstrating their effectiveness and convergence properties through real and simulated data, highlighting the copula's flexible distribution modeling.

Contribution

It proposes EM algorithms for Bernstein copula estimation, providing convergence proofs and asymptotic analysis, with practical demonstrations on real and simulated datasets.

Findings

EM algorithms converge locally

Bernstein copula models diverse distributions

Algorithms perform well on real data

Abstract

A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data.