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, we discuss the notions of variance and covariance of set-valued and interval-valued random variables. Then, we give the definition of the intervalvalued 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 simulation experiments and an application example regarding temperature of cities affected by their latitude, which illustrates the application of our model.