# A Linear Model for Interval-valued Data

arXiv: https://arxiv.org/abs/1506.03541 · HTML: https://mlsanity.com/paper/1506.03541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2015.

## Built on by (most cited first, 1 of 1)

- [Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression](https://mlsanity.com/paper/2104.07245/) (2021)

## Abstract (arXiv)

Interval-valued linear regression has been investigated for some time. One of the critical issues is optimizing the balance between model flexibility and interpretability. This paper proposes a linear model for interval-valued data based on the affine operators in the cone C =  (x, y) ∈ ℝ2 | x ≤ y. The resulting new model is shown to have improved flexibility over typical models in the literature, while maintaining a good interpretability. The least squares (LS) estimators of the model parameters are provided in a simple explicit form, which possesses a series of nice properties. Further investigations into the LS estimators shed light on the positive restrictions of a subset of the parameters and their implications on the model validity. A simulation study is presented that supports the theoretical findings. An application to a real data set is also provided to demonstrate the applicability of our model.