Lasso-based linear regression for interval-valued data

In regression analysis the relationship between one response and a set of explanatory variables is investigated. The (response and explanatory) variables are usually single-valued. However, in several real-life situations, the available information may be formalized in terms of intervals. An interval-valued datum can be described by the midpoint (its center) and the radius (its half width). Here, limiting our attention to the linear case, regression analysis for interval-valued data is studied. This is done by considering two linear regression models. One model investigates the relationship between the midpoints of the response variable and of the explanatory variables, whereas the other one analyzes the relationship between the radii. The two models are related by considering the same regression coefficients, i.e. the same linear relationship is assumed for the midpoints and the radii. However, in some cases, this assumption may be too restrictive. To overcome this drawback, additive coefficients for the model of the radii are introduced and their magnitude is tuned according to the Lasso technique allowing us to set to zero some of these additive coefficients. In order to show how the proposed method works in practice the results of an application to real-life data are discussed.