Lasso-constrained regression analysis for interval-valued data

A new method of regression analysis for interval-valued data is proposed. The 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 and the other one for the radii. The estimation problem is approached by introducing Lasso-based constraints on the regression coefficients. This can improve the prediction accuracy of the model and, taking into account the nature of the constraints, can sometimes produce a parsimonious model with a common subset of regression coefficients for the midpoint and the radius models. The effectiveness of our method, called Lasso-IR (Lasso-based Interval-valued Regression), is shown by a simulation experiment and some applications to real data.