Regression model for interval-valued variables based on copulas

Abstract

In real problems, it is usual to have the available data presented as intervals. Therefore, different approaches have been proposed to obtain a regression model for this new type of data. In this paper, we represent the interval-valued response variable $Z=[Y_{\mathrm{L}},Y_{\mathrm{U}}]$ as a bivariate random vector and we consider the copula's theory to propose a general bivariate distribution for Z, creating a more flexible random component to the model. Inference techniques and a residual definition based on deviance are considered, as well as applications to synthetic and real data sets that demonstrate the usefulness of the proposed approach. The new method is also compared with other methods reported in the literature.

Keywords:

• interval variables
• regression model
• copulas
• Monte Carlo
• deviance

AMS Subject Classification:

• 62J99
• 62N02
• 65G40

Acknowledgments

We would like to thank the anonymous referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

We would like to thank the Brazilian agencies (CNPq and CAPES) for their financial support.