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.
翻译:近些年来,人们越来越多地研究间隔值数据的回归方法。随着大多数现有工作侧重于线性模型,必须注意到,实践中的许多问题在性质上并非线性,因此,为间隔值数据开发非线性回归工具至关重要。在本文中,我们提议对间隔值数据采用基于树的回归方法,该方法完全适用于线性和非线性问题。与线性回归模型不同,线性回归模型通常需要额外的限制以确保预测间隔长度的假设性,拟议方法以非对称方式估算回归函数,因此,预测长度自然是正的,没有任何限制。进行了模拟研究,将我们的方法与在线性和非线性环境下流行的间隔值数据的现有回归模型进行比较。此外,我们采用方法分析道琼斯工业平均指数及其组成部分存量的价格范围数据时,提出了真正的数据实例。