Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets.

需要区间值数据来管理与测量相关的不确定性，或代表一组个体的复杂对象的描述所固有的可变性。许多适用于描述复杂对象可变性的区间变量的回归方法已经可用。然而，对同时考虑完整区间信息并抵抗区间异常值观察的方法的关注较少，即使在区间值数据集上频繁出现非典型观察也是如此。本文提出了一种新的区间变量稳健线性回归方法，其中中心或半径中存在异常值会惩罚中心和半径回归模型。而且，在中心和半径上都有异常值的区间观察比那些只在中心（或半径）有异常值的观察更受惩罚。此外，本文提供了一种合适的迭代算法来估计所提出方法的参数。该算法在考虑中心和半径的信息的情况下估计中心（或半径）模型的参数。还介绍了迭代算法的收敛性和时间复杂度。最后，将新方法的性能与一些以前的稳健回归方法进行比较，并在合成和真实区间值数据集上进行评估。本文提供了一种合适的迭代算法来估计所提出方法的参数。该算法在考虑中心和半径的信息的情况下估计中心（或半径）模型的参数。还介绍了迭代算法的收敛性和时间复杂度。最后，将新方法的性能与一些以前的稳健回归方法进行比较，并在合成和真实区间值数据集上进行评估。本文提供了一种合适的迭代算法来估计所提出方法的参数。该算法在考虑中心和半径的信息的情况下估计中心（或半径）模型的参数。还介绍了迭代算法的收敛性和时间复杂度。最后，将新方法的性能与一些以前的稳健回归方法进行比较，并在合成和真实区间值数据集上进行评估。