Robust regression for interval-valued data based on midpoints and log-ranges

Flexible modelling of interval-valued data is of great practical importance with the development of advanced technologies in current data collection processes. This paper proposes a new robust regression model for interval-valued data based on midpoints and log-ranges of the dependent intervals, and obtains the parameter estimators using Huber loss function to deal with possible outliers in a data set. Besides, the use of logarithm transformation avoids the non-negativity constraints for the traditional modelling of ranges, which is beneficial to the flexible use of various regression methods. We conduct extensive Monte Carlo simulation experiments to compare the finite-sample performance of our model with that of the existing regression methods for interval-valued data. Results indicate that the proposed method shows competitive performance, especially in the data set with the existence of outliers and the scenarios where both midpoints and ranges of independent variables are related to those of the dependent one. Moreover, two empirical interval-valued data sets are applied to illustrate the effectiveness of our method.