Interval-Valued Linear Model

DOI

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - 10.2991/ijcis.2015.8.1.10
ID  - Wang2015
ER  -