论文标题
基于树间隔数据的基于树的回归
Tree-based Regression for Interval-valued Data
论文作者
论文摘要
近年来，对间隔值数据的回归方法进行了越来越多的研究。由于大多数现有作品都集中在线性模型上，因此必须注意，实践中的许多问题本质上都是非线性的，因此开发用于间隔值数据的非线性回归工具至关重要。在本文中，我们提出了一种基于树的回归方法，用于间隔值数据，该方法非常适用于线性和非线性问题。与通常需要其他约束以确保预测间隔长度的阳性的线性回归模型不同，该方法以非参数方式估算回归函数，因此预测的长度自然是正面的，而没有任何约束。进行了一项仿真研究，将我们的方法与线性和非线性设置下的间隔值数据的流行回归模型进行了比较。此外，提出了一个真实的数据示例，我们将我们的方法应用方法来分析道琼斯工业平均指数及其组件股票的价格范围数据。
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.
