International Journal of Computational Intelligence Systems

Volume 8, Issue 1, January 2015, Pages 114 - 127

Interval-Valued Linear Model

Authors
Xun Wang, Shoumei Li, Thierry Denœux
Corresponding Author
Xun Wang
Received 30 May 2014, Accepted 15 July 2014, Available Online 1 January 2015.
DOI
https://doi.org/10.2991/ijcis.2015.8.1.10How to use a DOI?
Keywords
interval-valued linear model, least square estimation, best binary linear unbiased estimation, D metric
Abstract
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.
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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
8 - 1
Pages
114 - 127
Publication Date
2015/01/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
https://doi.org/10.2991/ijcis.2015.8.1.10How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Xun Wang
AU  - Shoumei Li
AU  - Thierry Denœux
PY  - 2015
DA  - 2015/01/01
TI  - Interval-Valued Linear Model
JO  - International Journal of Computational Intelligence Systems
SP  - 114
EP  - 127
VL  - 8
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.2015.8.1.10
DO  - https://doi.org/10.2991/ijcis.2015.8.1.10
ID  - Wang2015
ER  -