A Linear Model for Interval-valued Data
| Autor: | Sun, Yan, Ralescu, Dan |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\mathcal{C} = \{ (x, y) \in \mathbb{R}^2 | x \leq y\}$. 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. Comment: 18 pages, 5 figures |
| Databáze: | arXiv |
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