Interval-Valued Linear Model
This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, notions of variance and covariance of set-valued and interval-valued random var...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2015-01-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25868588.pdf |
| _version_ | 1818038014700421120 |
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| author | Xun Wang Shoumei Li Thierry Denœux |
| author_facet | Xun Wang Shoumei Li Thierry Denœux |
| author_sort | Xun Wang |
| collection | DOAJ |
| description | This paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, notions of variance and covariance of set-valued and interval-valued random variables are introduced. Then, we give the definition of the interval-valued linear model and its least square estimator (LSE), as well as some properties of the LSE. Thirdly, we show that, whereas the best linear unbiased estimation does not exist, the best binary linear unbiased estimator exists and it is the LSE. Finally, we present simulation experiments and an application example regarding temperatures of cities affected by their latitude, which illustrates the application of the proposed model. |
| first_indexed | 2024-12-10T07:36:00Z |
| format | Article |
| id | doaj.art-18454e3989d8429690a960cfc697cb0e |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-12-10T07:36:00Z |
| publishDate | 2015-01-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-18454e3989d8429690a960cfc697cb0e2022-12-22T01:57:25ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832015-01-018110.2991/ijcis.2015.8.1.10Interval-Valued Linear ModelXun WangShoumei LiThierry DenœuxThis paper introduces a new type of statistical model: the interval-valued linear model, which describes the linear relationship between an interval-valued output random variable and real-valued input variables. Firstly, notions of variance and covariance of set-valued and interval-valued random variables are introduced. Then, we give the definition of the interval-valued linear model and its least square estimator (LSE), as well as some properties of the LSE. Thirdly, we show that, whereas the best linear unbiased estimation does not exist, the best binary linear unbiased estimator exists and it is the LSE. Finally, we present simulation experiments and an application example regarding temperatures of cities affected by their latitude, which illustrates the application of the proposed model.https://www.atlantis-press.com/article/25868588.pdfinterval-valued linear modelleast square estimationbest binary linear unbiased estimationD metric |
| spellingShingle | Xun Wang Shoumei Li Thierry Denœux Interval-Valued Linear Model International Journal of Computational Intelligence Systems interval-valued linear model least square estimation best binary linear unbiased estimation D metric |
| title | Interval-Valued Linear Model |
| title_full | Interval-Valued Linear Model |
| title_fullStr | Interval-Valued Linear Model |
| title_full_unstemmed | Interval-Valued Linear Model |
| title_short | Interval-Valued Linear Model |
| title_sort | interval valued linear model |
| topic | interval-valued linear model least square estimation best binary linear unbiased estimation D metric |
| url | https://www.atlantis-press.com/article/25868588.pdf |
| work_keys_str_mv | AT xunwang intervalvaluedlinearmodel AT shoumeili intervalvaluedlinearmodel AT thierrydenœux intervalvaluedlinearmodel |