A regularized MM estimate for interval-valued regression

In real life, we usually encounter with interval-valued data when analyzing imprecise data or massive data sets. In this paper, a regularized interval MM estimate (RIMME) for interval-valued regression is proposed. In order to mitigate the mathematical incoherence of the predicted intervals, a regularized term is introduced to penalize the number of crossing intervals. Therefore, the proposed method can achieve a good balance between the prediction accuracy and mathematical coherence of the predicted intervals. To evaluate the performance of RIMME, a simulation study and three real data sets are examined. Experimental results illustrate that our method outperforms five commonly used methods in almost all cases.