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

• Published in: Information sciences Vol. 199; pp. 109 - 124
• Main Authors: Sinova, Beatriz, Colubi, Ana, Gil, Marı´a Ángeles, González-Rodrı´guez, Gil
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.09.2012
• Subjects: Generalized mid/spread metric; Interval arithmetic; Linear regression analysis; Rrandom interval-valued set; t-Vector function; Rrandom interval-valued set; Linear regression analysis; Generalized mid/spread metric; t-Vector function; Interval arithmetic
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2012.02.040

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.