Nonlinear regression applied to interval-valued data

This paper introduces a nonlinear regression model to interval-valued data. The method extends the classical nonlinear regression model in order to manage interval-valued datasets. The parameter estimates of the nonlinear model considers some optimization algorithms aiming to identify which one presents the best accuracy and precision in the prediction task. A detailed prediction performance study comparing the proposed nonlinear method and other linear regression methods for interval variables is presented based on K-fold cross-validation scheme with synthetic interval-valued datasets generated on a Monte Carlo framework. Moreover, two suitable real interval-valued datasets are considered to illustrate the usefulness and the performance of the approaches presented in this paper. The results suggested that the use of the nonlinear method is suitable for real datasets, as well as in the Monte Carlo simulation study.