Tree-based Regression for Interval-valued Data

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore development of nonlinear regression tools for interval-valued data is crucial. In this paper, we propose a tree-based regression method for interval-valued data, which is well applicable to both linear and nonlinear problems. Unlike linear regression models that usually require additional constraints to ensure positivity of the predicted interval length, the proposed method estimates the regression function in a nonparametric way, so the predicted length is naturally positive without any constraints. A simulation study is conducted that compares our method to popular existing regression models for interval-valued data under both linear and nonlinear settings. Furthermore, a real data example is presented where we apply our method to analyze price range data of the Dow Jones Industrial Average index and its component stocks.