Interval arithmetic-based simple linear regression between interval data: Discussion and sensitivity analysis on the choice of the metric

The prediction of a response random interval-valued set from an explanatory one has been examined in previous developments. These developments have considered an interval arithmetic-based linear model between the random interval-valued sets and a least squares regression analysis. The least squares approach involves a generalized L2-metric between interval data; this metric weights squared distances between data location (mid-points/centers) and squared distances between data imprecision (spread/radius). As a consequence, estimators of the parameters in the linear model depend on the choice of the weights in the metric. To investigate about a suitable choice of weighting in the generalized mid/spread metric, a theoretical conclusion is first obtained. Finally, the impact of varying the weights is discussed by considering a Monte Carlo simulation study.