Estimating Multivariate Discrete Distributions Using Bernstein Copulas

Abstract

Measuring the dependence between random variables is one of the most fundamental problems in statistics, and therefore, determining the joint distribution of the relevant variables is crucial. Copulas have recently become an important tool for properly inferring the joint distribution of the variables of interest. Although many studies have addressed the case of continuous variables, few studies have focused on treating discrete variables. This paper presents a nonparametric approach to the estimation of joint discrete distributions with bounded support using copulas and Bernstein polynomials. We present an application in real obsessive-compulsive disorder data.

Keywords

• Bernstein polynomial
• copula
• nonparametric inference
• Aitchison’s distance