A spatial Durbin model for interval-valued data with t-distribution

Abstract

Interval-valued data have received much attention due to their wide applications in finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume that the observations are mutually independent, which can not be adapted to scenarios where individuals are spatially correlated. We propose a new linear model to account for areal-type spatial dependencies present in interval-valued data. Specifically, two spatial Durbin models are separately built for the centers and log-ranges of the interval-valued response. To make the new model more robust to heavy-tailed noise, we assume the error term follows a t-distribution. The parameters are obtained using an expectation-maximization (EM) algorithm. Numerical experiments are designed to examine the performance of the proposed method. We also use a weather dataset to demonstrate the usefulness of our model.