Some regression models for analyzing relationships between random intervals (i.e., random variables taking intervals as outcomes) are presented. The proposed approaches are extensions of previous existing models and they account for cross relationships between midpoints and spreads (or radii) of the intervals in a unique equation based on the interval arithmetic. The estimation problem, which can be written as a constrained minimization problem, is theoretically analyzed and empirically tested. In addition, numerically stable general expressions of the estimators are provided. The main differences between the new and the existing methods are highlighted in a real-life application, where it is shown that the new model provides the most accurate results by preserving the coherency with the interval nature of the data.

中文翻译：

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随机区间的多个线性回归模型：一套算术方法

提出了一些用于分析随机区间（即以区间为结果的随机变量）之间关系的回归模型。所提出的方法是对先前现有模型的扩展，并且它们基于间隔算法在唯一方程式中考虑了间隔的中点和范围（或半径）之间的交叉关系。可以写为约束最小化问题的估计问题在理论上进行了分析和经验检验。另外，提供了估计器的数值稳定的一般表达式。新方法和现有方法之间的主要区别在一个实际应用中得到了强调，该应用表明，新模型通过保留数据间隔性质的一致性提供了最准确的结果。