Local Dependence in Bivariate Copula Models with Beta Marginals

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Eirini Koutoumanou*+ and Angela Wade and Mario Cortina-Borja
• Companies: University College London Institute of Child Health and University College London Institute of Child Health and University College London Institute of Child Health
• Keywords: copulas ; bivariate beta ; local dependence function

Abstract

When exploring the association between two random variables, X1 and X2, often scalar measures of correlation cannot describe adequately the dependence structure between them. One way to characterize the nature of their joint variation is by localizing the strength of the association along the range of (X1, X2); this can be done using the local dependence function (LDF). The LDF measures the correlation between X1 and X2 in a neighbourhood of any point (x1,x2) in the domain of the bivariate density function. Local dependence can be particularly useful when exploring the association between marginals in bivariate Beta distributions defined through copulas. These models capture a large variety of shapes in the unit square and are useful representations of joint outcome variables measured on bounded scales. We formulate expressions for the joint density, Pearson's correlation coefficient, and local dependence function for copula models with beta marginals. We also illustrate local dependence analyses from fitting these models to [0,1]-bounded data.