Linear regression analysis for interval-valued data based on the Lasso technique

A new method for linear regression analysis of interval-valued data is proposed. In particular, the linear relationship between an interval-valued response variable and a set of interval-valued explanatory variables is investigated by considering two regression models, one for the midpoints (the locations of the intervals) of the response and explanatory variables and the other one for the radii (the imprecision). The regression coefficients of the two models are estimated in such a way that those for the midpoints are close to the corresponding ones for the radii as much as possible. Taking inspiration from the Lasso technique this is done by fixing a threshold expressing the maximum allowed level of diversity between the two sets of regression coefficients. The results of a simulation experiment and some applications to real data are reported in order to show the usefulness of the proposed method, called Lasso-IR (Lasso-based Interval-valued Regression).