On Linear Regression for Interval-valued Data in ${\mathcal{K}}_{\mathcal{C}}\left(\mathbb{R}\right)$

Abstract

It has been some time since interval-valued linear regression was investigated. In this paper, we focus on linear regression for interval-valued data within the framework of random sets. The model we propose generalizes a series of existing models. We establish important properties of the model in the space of compact convex subsets of $\mathbb{R}$, analogous to those for the classical linear regression. Furthermore, we carry out theoretical investigations into the least squares estimation that is widely used in the literature. A simulation study is presented that supports our theorems. Finally, an application to a climate data set is provided to demonstrate the applicability of our model.

20 pages, 4 figures