Xun Wang, Shoumei Li, Thierry Denoeux

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Interval-Valued Linear Model

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, we discuss the notions of variance and covariance of set-valued and interval-valued random variables. Then, we give the definition of the interval-valued linear model and its least square estimation, as well as some properties of the least square estimation. Thirdly, we show that, whereas the best linear unbiased estimation does not exist, the best binary linear unbiased estimator exists and it is just the least square estimator. Finally, we present a simulation experiment and an application example regarding temperature of cities affected by their latitude, which illustrates the application of our model.

Keywords

Interval-valued linear model, Least square estimation, Best binary linear unbiased estimation, D_p metric

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E-mail addresses

Xun Wang		xunwang00@gmail.com
Shoumei Li		lisma@bjut.edu.cn
Thierry Denoeux		thierry.denoeux@hds.utc.fr