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, 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.

Keywords

• interval-valued linear model
• least square estimation
• best binary linear unbiased estimation
• D metric